Actually, I don't think I was evading anything, but I did notice that you evaded (perhaps unintentionally) my question of whether you would have brought your little child to Christ to be blessed.
Far from evading anything, I was simply demonstrating an aspect of the Gospels where children were receiving grace from Christ that they didn't understand. Which, from an Orthodox point of view, is the real question about whether children should receive baptism, chrismation, and Holy Communion.
You are correct that Scripture doesn't explicitly say that infants were baptized at that time -- it is silent, but you already know the references that are used to show that it may be implied. I won't repeat them.
The Church was very different in the early years, in that the focus was on the conversion of adults. We believe that with the onset of families coming into the Church, all were baptized in many cases, but I can't prove that.
I would also point out that the only practice that is criticized in the patristic writings (although sometimes it is also recommended) is the practice of waiting a long time for baptism -- even at one's deathbed (such as the Emperor St. Constantine) out of concern that this was one's only shot at a full forgiveness of sins.
It has been said that part of St. Constantine's motivation not to formally join the Church that he promoted so vigorously and studied arduously, was that he felt that as emperor, he had to do so many things that were dangerous to the soul: execute and imprison people, kill people by waging war, etc...
My point is that while there was controversy about how long one waited, there is no record of any controversy about the baptism of infants. Again, this is a passive witness, not an active one, even if you were inclined to look at history as a useful tool in understanding the Apostolic practice.
Baptists are being consistent in their practice of adult baptism only if the criterion is whether it is explicitly spelled out in Scripture.
I would ask, though, that you take every other aspect of Baptist practice and mentally apply the same criterion. Imagine things about how you worship and live the Christian life, that if you were to change them, people would raise a ruckus -- and then try to find whether they are explicitly spelled out in the NT in the life of the Church.
Maybe you have a practice of people coming forward and kneeling at the front of the church -- is that in the Bible? Is having a specific church building at all in the Bible? Are having crosses on steeples in the Bible? Are having rows of pews in the Bible? Is having a pulpit in the Bible?
Is there a single instance of someone leading another person in a "sinner's prayer" in the Bible? By your criteria, if it isn't explicitly spelled out in the Bible, it shouldn't be done. Given the centrality in most fundamentalist practices of leading someone in the sinner's prayer -- it is the defining moment of when someone was saved -- wouldn't the NT look much different, and have some explicit examples of this being done? I think you get my drift. We all have traditions, and practices not explicitly spelled out in the Scriptures -- we just don't all recognize them as such.