Infant Baptism wasn't practiced by the Very Early Church.

The Didache is often considered the earliest Extra Biblical Writing.  Chapter 7 is its instructions for Baptism.

“And concerning baptism, baptize this way: Having first said all these things, baptize into the name of the Father, and of the Son, and of the Holy Spirit, in living water. But if you have no living water, baptize into other water; and if you cannot do so in cold water, do so in warm. But if you have neither, pour out water three times upon the head into the name of Father and Son and Holy Spirit. But before the baptism let the baptizer fast, and the baptized, and whoever else can; but you shall order the baptized to fast one or two days before.”

And we also see a description of how Baptism works in Justin Martyr’s First Apology chapter 61.

“I will also relate the manner in which we dedicated ourselves to God when we had been made new through Christ; lest, if we omit this, we seem to be unfair in the explanation we are making. 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 Saviour Jesus Christ, and of the Holy Spirit, they then receive the washing with water. For Christ also said, Unless you be born again, you shall not enter into the kingdom of heaven. John 3:5 Now, that it is impossible for those who have once been born to enter into their mothers' wombs, is manifest to all. And how those who have sinned and repent shall escape their sins, is declared by Esaias the prophet, as I wrote above; he thus speaks: Wash you, make you clean; put away the evil of your doings from your souls; learn to do well; judge the fatherless, and plead for the widow: and come and let us reason together, says the Lord. And though your sins be as scarlet, I will make them white like wool; and though they be as crimson, I will make them white as snow. But if you refuse and rebel, the sword shall devour you: for the mouth of the Lord has spoken it. Isaiah 1:16-20

And for this [rite] 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 Lord of the universe; he who leads to the laver the person that is to be washed calling him by this name alone. For no one can utter the name of the ineffable God; and if any one dare to say that there is a name, he raves with a hopeless madness. And this washing is called illumination, because they who learn these things are illuminated in their understandings. And in the name of Jesus Christ, who was crucified under Pontius Pilate, and in the name of the Holy Ghost, who through the prophets foretold all things about Jesus, he who is illuminated is washed.”

In both cases clearly only Baptism of Adults are being described.  If Infant Baptism already existed then some distinctions for how that would obviously work differently would need to be made.  But none of these instructions would need to be different for Adults raised in the Faith after reaching a certain rather than Converts.

Pedo-Baptists try to infer Infant Baptism in various things said by Irenaeus or the Martyrdom of Polycarp or the Shepherd of Hermas but they are all things with other explanations.  

Largely they are tied to assumptions about Water Baptism that Credo-Baptists dispute, but I do think those eros actually came first and Infant Baptism is the symptom.  Treating every Biblical reference to Baptism as about Water Baptism when the most important are not about that.  And misunderstanding Colossians as saying Circumcision replaces Baptism when in fact Paul's point is that for both the physical ritual is merely a symbol.

The earliest provable unambiguous references to Infant Baptism are in the Third Century, Tertullian and Origen, then Cyprian was the first to really stress it as obligatory.

I agree that the Novatians were Credo-Baptists even though I disagree with them on their defining doctrine, but not the Donatists.

At least some of the Britons were still Credo-Baptists as late as the early 7th Century.