We offer the following quotations from the first volume of the Ante Nicene Fathers. The authors represented here lived contiguous to the time of the Apostles. At least one was a personal disciple of John (Ignatius).
Ignatius appeals to Romans 6:5:"Wherefore also, you appear to me to live not after the manner of men, but according to Jesus Christ, who died for us, in order that, by believing in His death,you may by baptism be made partakers of His resurrection."(Ignatius, Epistle to the Trallians, II)
Baptism Unites us to Christ's Death (Romans 6:5). "For if there is one God of the universe, the Father of Christ, “of whom are all things;” and one Lord Jesus Christ, our [Lord], “by whom are all things;” and also one Holy Spirit, who wrought in Moses, and in the prophets and apostles; and also one baptism, which is administered that we should have fellowship with the death of the Lord; and also one elect Church; there ought likewise to be but one faith in respect to Christ. For “there is one Lord, one faith, one baptism; one God and Father of all, who is through all, and in all.” (Ignatius, Epistle to the Philippians, I)
The OT Foreshadows Baptism for the Remission of Sins (Acts 2:38). "Let us further inquire whether the Lord took any care to foreshadow the water [of baptism] and the cross. Concerning the water, indeed, it is written, in reference to the Israelites, that they should not receive that baptism which leads to the remission of sins, but should procure another for themselves. The prophet therefore declares, “Be astonished, O heaven, and let the earth tremble at this, because this people hath committed two great evils: they have forsaken Me, a living fountain, and have hewn out for themselves broken cisterns ”. (Epistle of Barnabas, XI)
"Regeneration" (New Birth) Takes Place at Baptism (cf. John 3:3-5 & Titus 3:5). "As many as are persuaded and believe that what we teach and say is true, and undertake to be able to live accordingly, are instructed to pray and to entreat God with fasting, for the remission of their sins that are past, we praying and fasting with them. Then they are brought by us where there is water, and are regenerated in the same manner in which we were ourselves regenerated. For, in the name of God, the Father and Lord of the universe, and of our Savior Jesus Christ, and of the Holy Spirit,they then receive the washing with water. For Christ also said, “Except ye be born again, ye shall not enter into the kingdom of heaven.” Now, that it is impossible for those who have once been born to enter into their mothers’ wombs, is manifest to all. ... And for this [baptism] we have learned from the apostles this reason. Since at our birth we were born without our own knowledge or choice, by our parents coming together, and were brought up in bad habits and wicked training; in order that we may not remain the children of necessity and of ignorance, but may become the children of choice and knowledge, and may obtain in the water the remission of sins formerly committed, there is pronounced over him who chooses to be born again, and has repented of his sins, the name of God the Father ... And in the name of Jesus Christ, ... and in the name of the Holy Ghost..." (Justin, First Apology, LXI)
"And this food is called among us Eujcariatia [the Eucharist], of which no one is allowed to partake but the man who believes that the things which we teach are true, and who has been washed with the washing that is for the remission of sins, and unto regeneration, and who is so living as Christ has enjoined."(Justin First Apology, LXVI)
The Gnostics Pervert Baptism "It happens that their tradition respecting redemption is invisible and incomprehensible, as being the mother of things which are incomprehensible and invisible; and on this account, since it is fluctuating, it is impossible simply and all at once to make known its nature, for every one of them hands it down just as his own inclination prompts. Thus there are as many schemes of “redemption” as there are teachers of these mystical opinions. And when we come to refute them, we shall show in its fitting-place, that this class of men have been instigated by Satan to a denial of that baptism which is regeneration to God, and thus to a renunciation of the whole [Christian] faith." (Irenaeus, Against Heresies, Bk. I, ch xxi)
The Healing of Naaman Prefigured Christian Baptism “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.” (Irenaeus, Frag. XXXIV)
These are the earliest quotes. We could produce many more from later writers. However, later writers do not prove the earliest tradition. What is apparent in any survey of the early Church's view of baptism is its unanimous opinion.
No writer suggested that baptism takes place after the new birth. Baptism was universally considered to be the point where regeneration occurs.