Different eras tend to raise questions specific to that moment. Early on, the church moved in the direction of baptismal regeneration, equating giving the sign with giving the thing signified, even to having the sign confer the reality. They believed this about adults receiving baptism, which is why it comes into vogue to delay baptism for adult converts. It is hard even to imagine how infant baptism could have arisen de novo as a post-apostolic practice, in a context where serious Christians were putting off baptism until the last possible moment. Clearly the practice of IB has an origin earlier than the delay of baptism, and in fact Tertullian avers the practice of IB is apostolic in origin.
But by the time there are authors writing about church practices, including baptism, baptismal regeneration (likely arising just from the habit of using straight biblical language that doesn't drive thick conceptual wedges between such a sign and its proper signification) has begun to dominate. The questions people are starting to ask concern matters like, "why not get the most sin-removal possible from this rite?" and "baptism is only for once, so what happens to the backsliders who want to return to the faith and the church?" Meanwhile, children are still being baptized! It is alleged that at first only dying infants were probably baptized, on account of belief in baptismal regeneration, but this totally presumes it was introduced (without written objections appearing anywhere) a post-apostolic practice, to take advantage of a benefit that was known to be available in fact without any baptism. In other words, the idea of the special necessity of baptism for regeneration has to develop, and cannot be read-back into the earliest regard for the regenerating and sin-removing benefit of the ritual.
It's just as false to import a full-blown baptismal regeneration concepts into earliest expressions from Church Fathers, who are frequently just using the terms of Scripture without any intentional equivocation. They aren't driving wedges between sign and signification, because these things belong together. It is reasonable to treat and regard those who bear the sign as if they have or are bound to demonstrate possession of the signification, if at another time than this instant. Normal theological development of problems, both in doctrine and in practice, demand at a certain time clear answers be given; which is accomplished by going back to Scripture and creating fine theological statements--creed postulates--that form dividing lines between those with accurate understanding and use of biblical terms, and those who may cling to the ancient words, but impose a false meaning on them.
The Reformed, with voices like Calvin's, are usually content to say: we don't know the moment of anyone's regeneration. It is not a question for humans to answer, since the Spirit blows when and where he pleases. He wills for us to connect in our minds the signs we see with the spiritual meaning tied to the sign. Perhaps God starts his quickening process around the time of someone's baptism, be he 2 decades old, or 2 days. That's not our concern. The discipleship process is our concern, for men of 20yrs or for a babe of 20mos. Make disciples, by baptizing and teaching them. We are not concerned whether there is an antecedent or coincident condition of "real" regeneration. What we hope to see is evidence of repentance and faith, which is the life of the regenerated, all which should be baptized.