Your question is based on three false premises. Contrary to your assumptions, the New Testament does not only speak of two Sacraments, and neither does it teach that Baptism and Communion are "only memorials". Furthermore, your question assumes that if something is not explicitly taught in Scripture that we should reject it, but this doctrine of Sola Scriptura is itself not only not taught in Scripture, but is in fact directly contradicted by Scripture (e.g., 2 Thessalonians 2:15). See my article on Sola Scriptura for more on that subject.
How many Sacraments are there?
In the service for the reception of converts from heterodox confessions, one of the affirmations that a convert is asked to affirm is: "Dost thou believe and confess that there are seven Sacraments of the New Testament, to wit: Baptism, Chrismation, the Eucharist, Confession, the Priesthood, Marriage, and Anointing with Oil, instituted by the Lord Christ and his Church, to the end that, through their operation and reception, we may obtain blessings from on high?"
Do we find them in the Bible?
Yes, we do. Let's consider each of the Sacraments aside from Baptism and the Eucharist:
1. Chrismation: One place we find Chrismation mentioned in Scripture is in 2 Corinthians 1:21-22: "Now he who establisheth us with you in Christ, and hath anointed us, is God; Who hath also sealed us, and given the earnest of the Spirit in our hearts." And 1 John 2:20: "But ye have an anointing from the Holy One, and ye know all things." We also see in the book of Acts that the Holy Spirit was imparted by the laying on of hands of the Apostles (Acts 8:14-17; Acts 19:1-7). And not only that, but we find Chrismation affirmed as a sacrament in the earliest writings of the Church (e.g., Tertullian's Treatise on Baptism (ca. 200 A.D.), 7:1; The Apostolic Tradition (ca. 215 A.D.) of St. Hippolytus 21:19-22; St. Cyril of Jerusalem's Catechetical Lecture 21 (on Chrism)).
2. Confession: When Christ appeared to the Disciples after the Resurrection, we are told: "And when he had said this, he breathed on them, and saith unto them, Receive ye the Holy Spirit: Whose soever sins ye remit, they are remitted unto them; and whose soever sins ye retain, they are retained" (John 20:22-23). Obviously for this to have meaning, there would have to be some occasion in which the apostles, or their successors would either confer forgiveness, or choose not to confer it. And this clearly was not merely a "memorial", because Christ clearly says that Heaven will confirm their decision.
3. Ordination: It is clear from Scripture that there were offices in the Church (deacon, presbyter, bishop), and so there was some way that the Church appointed people to these offices. We see, for example, in Act 6:6, when the Apostles had selected the first deacons the seven men chosen were "set before the apostles: and when they had prayed, they laid their hands on them." St. Paul admonished St. Timothy that he "Lay hands suddenly on no man" (1 Timothy 5:22) -- in other words, he was to be careful about who he ordained, lest he "be partaker of other men's sins..." There is such an abundance of testimony from the early Church on this that it hardly needs to be cited. But we see these three ranks of clergy in the Epistles of St. Ignatius of Antioch (who was a disciple of the Apostle John, and martyred in 112 A.D.): “Similarly, let everyone respect the deacons as Jesus Christ, just as they should respect the bishop, who is a model of the Father, and the presbyters as God’s council and as the band of the Apostles. Without these no group can be called a church” (Trallians 3:13).
4. Marriage is called a "covenant" in Scripture which has God Himself as a witness (Malachi 2:14): "Yet ye say, Wherefore? Because the Lord hath been witness between thee and the wife of thy youth, against whom thou hast dealt treacherously: yet is she thy companion, and the wife of thy covenant." St. Ignatius of Antioch, in his letter to St. Polycarp said that: " It becometh men and women too, when they marry, to unite themselves with the consent of the bishop, that the marriage may be after the Lord and not after concupiscence. Let all things be done to the honour of God" (Epistle to Polycarp 5:1). And Tertullian speaks of the sacrament of marriage in his treatise "To My Wife" (ca. 200 A.D.): "Whence are we to find (words) enough fully to tell the happiness of that marriage which the Church cements, and the oblation confirms, and the benediction signs and seals; (which) angels carry back the news of (to heaven), (which) the Father holds for ratified? For even on earth children do not rightly and lawfully wed without their fathers' consent" (To My Wife 2:8:4).
5: Holy Unction: We find this sacrament clearly described in James 5:14-15: "Is any sick among you? let him call for the elders of the church; and let them pray over him, anointing him with oil in the name of the Lord: And the prayer of faith shall save the sick, and the Lord shall raise him up; and if he have committed sins, they shall be forgiven him."
Christ taught his disciples that if they did not eat His Flesh and drink His Blood, they had no life in them (John 4:48-69), and even Martin Luther took Christ's words "this is My Body... this is My Blood" (Matthew 26:26-28) to mean that the Eucharist is literally, not merely figuratively, the Body and Blood of Christ.
St. Paul speaks of the Eucharist in two places in First Corinthians. In 1 Corinthians 10:16-17, he says:
"The cup of blessing which we bless, is it not the communion of the blood of Christ? The bread which we break, is it not the communion of the body of Christ? For we being many are one bread, and one body: for we are all partakers of that one bread."
And then in 11:23-30, he says:
"For I have received of the Lord that which also I delivered unto you, that the Lord Jesus the same night in which he was betrayed took bread: and when he had given thanks, he brake it, and said, Take, eat: this is my body, which is broken for you: this do in remembrance of me. After the same manner also he took the cup, when he had supped, saying, this cup is the new testament in my blood: this do ye, as oft as ye drink it, in remembrance of me. For as often as ye eat this bread, and drink this cup, ye do shew the Lord's death till he come. Wherefore whosoever shall eat this bread, and drink this cup of the Lord, unworthily, shall be guilty of the body and blood of the Lord. But let a man examine himself, and so let him eat of that bread, and drink of that cup. For he that eateth and drinketh unworthily, eateth and drinketh damnation to himself, not discerning the Lord's body. For this cause many are weak and sickly among you, and many sleep."
St. Paul says that the Eucharist is the communion of the Body and Blood of Christ, and that if we partake of it unworthily, we eat and drink damnation unto ourselves, because we have not discerned the Lord's Body, and so we are are "guilty of the Body and Blood of the Lord." That all seems awfully extreme if we are talking about a mere "memorial."
St. Ignatius of Antioch, who, once again, was a disciple of the Apostle John himself, and bishop of one of the most important centers of the early Church said of the Eucharist:
“Be zealous, then, in the observance of one Eucharist. For there is one flesh of our Lord Jesus Christ, and one chalice that brings union in His blood. There is one altar, as there is one bishop, with the priest and the deacons, who are my fellow workers” (Philadelphians 4:1).
“But consider those who are of a different opinion with respect to the grace of Christ which has come unto us, how they oppose the will of God…. They abstain from the Eucharist and from prayer, because they confess not the Eucharist to be the flesh of our Saviour Jesus Christ, which suffered for our sins, and which the Father, of His goodness raised up again. Those, therefore, who speak against the gift of God, incur death in the midst of their disputes. But it were better for them to treat it with respect, that they also might rise again” (Smyrneaens 6:2-7:1).
“Flee from divisions, as the beginning of evils. You must all follow the bishop, as Jesus Christ followed the Father, and follow the presbyters as you would the apostles; and respect the deacons as the commandment of God. Let no one do anything that has to do with the Church without the bishop. Only that Eucharist which is under the authority of the bishop (or whomever he himself designates) is to be considered valid. Wherever the bishop appears, there let the congregation be; just as wherever Jesus Christ is, there is the Catholic Church. It is not permissible either to baptize or to hold a love feast without the bishop. But whatever he approves is also pleasing to God, in order that everything you may do may be trustworthy and valid” (Smyrneans 8:1-2).
“Assemble yourselves together in common, every one of you severally, man by man, in grace, in one faith and one Jesus Christ, who after the flesh was of David's race, who is Son of Man and Son of God, to the end that ye may obey the bishop and presbytery without distraction of mind; breaking one bread, which is the medicine of immortality and the antidote that we should not die but live for ever in Jesus Christ" (Ephesians 20:2).
It doesn't sound like St. Ignatius thought the Eucharist was a mere "memorial."
As for Baptism, Christ said that those who believe and are baptized will be saved (Mark 16:16). St. Paul says that we are buried with Christ in Baptism so that we can be raised with Him (Romans 6:4), and that Baptism is the "circumcision made without hands" (Colossians 2:11). St. Peter said that the Ark of Noah was a type of Baptism, and that Baptism is "the antitype [that which was foreshadowed by the Type], which now save us" (1 Peter 3:20-21).
Only if you ignore what Christians have always taught about these sacraments could you reach the conclusions you assume in your question.
Are the Eucharist and Baptism merely "memorials"?
Christ taught his disciples that if they did not eat His Flesh and drink His Blood, they had no life in them (John 4:48-69), and even Martin Luther took Christ's words "this is My Body... this is My Blood" (Matthew 26:26-28) to mean that the Eucharist is literally, not merely figuratively, the Body and Blood of Christ.
St. Paul speaks of the Eucharist in two places in First Corinthians. In 1 Corinthians 10:16-17, he says:
"The cup of blessing which we bless, is it not the communion of the blood of Christ? The bread which we break, is it not the communion of the body of Christ? For we being many are one bread, and one body: for we are all partakers of that one bread."
And then in 11:23-30, he says:
"For I have received of the Lord that which also I delivered unto you, that the Lord Jesus the same night in which he was betrayed took bread: and when he had given thanks, he brake it, and said, Take, eat: this is my body, which is broken for you: this do in remembrance of me. After the same manner also he took the cup, when he had supped, saying, this cup is the new testament in my blood: this do ye, as oft as ye drink it, in remembrance of me. For as often as ye eat this bread, and drink this cup, ye do shew the Lord's death till he come. Wherefore whosoever shall eat this bread, and drink this cup of the Lord, unworthily, shall be guilty of the body and blood of the Lord. But let a man examine himself, and so let him eat of that bread, and drink of that cup. For he that eateth and drinketh unworthily, eateth and drinketh damnation to himself, not discerning the Lord's body. For this cause many are weak and sickly among you, and many sleep."
St. Paul says that the Eucharist is the communion of the Body and Blood of Christ, and that if we partake of it unworthily, we eat and drink damnation unto ourselves, because we have not discerned the Lord's Body, and so we are are "guilty of the Body and Blood of the Lord." That all seems awfully extreme if we are talking about a mere "memorial."
St. Ignatius of Antioch, who, once again, was a disciple of the Apostle John himself, and bishop of one of the most important centers of the early Church said of the Eucharist:
“Be zealous, then, in the observance of one Eucharist. For there is one flesh of our Lord Jesus Christ, and one chalice that brings union in His blood. There is one altar, as there is one bishop, with the priest and the deacons, who are my fellow workers” (Philadelphians 4:1).
“But consider those who are of a different opinion with respect to the grace of Christ which has come unto us, how they oppose the will of God…. They abstain from the Eucharist and from prayer, because they confess not the Eucharist to be the flesh of our Saviour Jesus Christ, which suffered for our sins, and which the Father, of His goodness raised up again. Those, therefore, who speak against the gift of God, incur death in the midst of their disputes. But it were better for them to treat it with respect, that they also might rise again” (Smyrneaens 6:2-7:1).
“Flee from divisions, as the beginning of evils. You must all follow the bishop, as Jesus Christ followed the Father, and follow the presbyters as you would the apostles; and respect the deacons as the commandment of God. Let no one do anything that has to do with the Church without the bishop. Only that Eucharist which is under the authority of the bishop (or whomever he himself designates) is to be considered valid. Wherever the bishop appears, there let the congregation be; just as wherever Jesus Christ is, there is the Catholic Church. It is not permissible either to baptize or to hold a love feast without the bishop. But whatever he approves is also pleasing to God, in order that everything you may do may be trustworthy and valid” (Smyrneans 8:1-2).
“Assemble yourselves together in common, every one of you severally, man by man, in grace, in one faith and one Jesus Christ, who after the flesh was of David's race, who is Son of Man and Son of God, to the end that ye may obey the bishop and presbytery without distraction of mind; breaking one bread, which is the medicine of immortality and the antidote that we should not die but live for ever in Jesus Christ" (Ephesians 20:2).
It doesn't sound like St. Ignatius thought the Eucharist was a mere "memorial."
As for Baptism, Christ said that those who believe and are baptized will be saved (Mark 16:16). St. Paul says that we are buried with Christ in Baptism so that we can be raised with Him (Romans 6:4), and that Baptism is the "circumcision made without hands" (Colossians 2:11). St. Peter said that the Ark of Noah was a type of Baptism, and that Baptism is "the antitype [that which was foreshadowed by the Type], which now save us" (1 Peter 3:20-21).
Only if you ignore what Christians have always taught about these sacraments could you reach the conclusions you assume in your question.
