So--why would it be identified as "Baptism"--or why would they have to be led to water--if it wasn't water baptism being referenced?
ST. JUSTIN MARTYR (inter A.D. 148-155)
Whoever is convinced and believes that what they are taught and told by us is the truth, and professes to be able to live accordingly, is instructed to pray and to beseech God in fasting for the remission of their former sins, while we pray and fast with them. Then they are led by us to a place where there is water; and there they are reborn in the same kind of rebirth in which we ourselves were reborn: In the name of God, the Lord and Father of all, and of our Savior Jesus Christ, and of the Holy Spirit, they receive the washing with water. For Christ said, "Unless you be reborn, you shall not enter into the kingdom of heaven." ...The reason for doing this, we have learned from the Apostles. (The First Apology 61)
The Early Church Fathers did cite John 3 as their reference for their beliefs connecting water baptism and the born again experience, and regeneration. That can easily be shown--as most all Early Church Fathers agreed on that doctrine:
ST. CYPRIAN OF CARTHAGE (c. 200 - 258 A.D.)