I have read the church fathers extensively and as far as I know there is not a single exception to the rule that all believed baptism was essential to salvation.  Even when infant baptism became common in the fourth century, still the teaching was, without exception, that salvation and forgiveness of sins occurs at baptism.  I might be wrong on this specific detail, but as far as I know, the first important Christian teacher to teach that baptism is not necessary to salvation was Ulrich Zwingli in the early sixteenth century.  I am including a few sample quotes on the subject from some of the earliest Christian authors.

Epistle of Barnabas  AD 110   We indeed descend into the water full of sins and defilement.  However, we come up, bearing fruit in our heart…

Shepherd of Hermas  AD 95

The seal, then, is the water.  They descend into the water dead, and they arise alive.

Irenaeus of Lyon AD 185

This class of men have been instigated by Satan to denial of that baptism which is regeneration to God.  Thus they have renounced the whole faith.

Tertullian of Carthage AD 205

Without baptism salvation is attainable by no one.

John Oakes

Follow-up from original questioner:

Here are some who do not believe that baptism is necessary: (at which point the questioner sends this link: https://carm.org/early-church-fathers-baptism

1. Baptism is Necessary for salvation
   1. Irenaeus (120?-200), “’And dipped himself,’ says [the Scripture], ‘seven times in Jordan.’ It was not for nothing that Naaman of old, when suffering from leprosy, was purified upon his being baptized, but it served as an indication to us. For as we are lepers in sin, we are made clean, by means of the sacred water and the invocation of the Lord, from our old transgressions; being spiritually regenerated as new-born babes, even as the Lord has declared: ‘Except a man be born again through water and the Spirit, he shall not enter into the kingdom of heaven.'” (Fragment, 34, A.D. 190).
   2. Origen (185-254), “The Church received from the Apostles the tradition of giving Baptism even to infants. For the Apostles, to whom were committed the secrets of divine mysteries, knew that there is in everyone the innate stains of sins, which must be washed away through water and the Spirit.” (Origen, Commentary on Romans, 5:9)
   3. Tertullian (155-220), “When, however, the prescript is laid down that ‘without baptism, salvation is attainable by none” (chiefly on the ground of that declaration of the Lord, who says, “Unless one be born of water, he hath not life.'” (On Baptism, 12:1, A.D. 203).
   4. Ambrose (340?-397), “The Church was redeemed at the price of Christ’s blood. Jew or Greek, it makes no difference; but if he has believed, he must circumcise himself from his sins [in baptism (Col. 2:11-12)] so that he can be saved . . . for no one ascends into the kingdom of heaven except through the sacrament of baptism . . . “Unless a man be born again of water and the Holy Spirit, he cannot enter the kingdom of God” (On Abraham 2:11:79-84).
2. Baptism is Not Necessary
   1. Clement of Rome (?-110), “And we, too, being called by His will in Christ Jesus, are not justified by ourselves, nor by our own wisdom, or understanding, or godliness, or works which we have wrought in holiness of heart; but by that faith through which, from the beginning, Almighty God has justified all men; to whom be glory for ever and ever. Amen.”  (The First Epistle of Clement to the Corinthians, Chapter 32).
   2. Polycarp (69-150), “by grace ye are saved, not of works,’ but by the will of God through Jesus Christ . . . If we please Him in this present world, we shall receive also the future world, according as He has promised to us that He will raise us again from the dead, and that if we live worthily of Him, ‘we shall also reign together with Him,’ provided only we believe . . . ” (Epistle to the Philippians, 1, 5, 8)
   3. Marius Victorinus (280-?): Every mystery which is enacted by our Lord Jesus Christ asks only for faith. The mystery was enacted at that time for our sake and aimed at our resurrection and liberation, should we have faith in the mystery of Christ and in Christ. For the patriarchs prefigured and foretold that man would be justified from faith. Therefore, just as it was reckoned as righteousness to Abraham that he had faith, so we too, if we have faith in Christ and every mystery of his, will be sons of Abraham. Our whole life will be accounted as righteous. Epistle to the Galatians, 1.3.7. Mark J. Edwards, ed., Ancient Christian Commentary on Scripture, New Testament VI: Galatians, Ephesians, Philippians (Downers Grove: InterVarsity Press, 1998), p. 39).

Response:

I notice that in Mr. Slick’s list, the passages he sites that say baptism in necessary in fact say that baptism is necessary, and the comments are unambiguous in that regard.  On the other hand, the passages he says say baptism is not necessary do not even mention baptism.  He does not give a single quote which says that baptism is not necessary.  This is because there are literally no quotes from the early church fathers which say what Mr. Slick says, which is that baptism is a work and that therefore baptism is not necessary.  Matt Slick claims that baptism is a work of man and he says that it is therefore not necessary.  What he lacks is a single quote which says either of these things.  I am sorry but Mr. Slick is not using the church father quotes faithfully.

From the quotes that Slick uses there are two possible conclusions:

1. These early church fathers were quite confused and did not really know what they were talking about.  They said that baptism is necessary out of one side of their mouths, but on the other side, they said that works are not needed, but baptism is a work of man, and therefore they contradicted themselves.

or

2. They knew exactly what they were talking about because the did not consider being baptized (a thing which is literally done to you) as a work.  Therefore when they said that baptism is necessary and that salvation is by grace not works, they were being logically consistent.

So, this gentleman uses quotes which make a very strong argument for the exact reverse of his conclusion.  The striking thing is that he does not see the obvious here.  Instead, he reads his own Calvinist conclusion into the evidence in a circular argument, reaching conclusion #1 above rather than the rather obvious conclusion #2 above.  Here is what the quotes show.  The early church was unanimous that we are saved by grace, through, faith, not by works.  They were also unanimous in their belief that baptism was a work of God and that salvation occurs upon baptism–it is the point in time that a person is forgiven of their sins.  Like I said in my response to your first question, this is the unanimous testimony of all early church fathers.

John Oakes