Upvote:1
In ancient times, children were considered adults around puberty. For the Jews, this would correspond with their bar/bat mitzvah, which even today is still the ceremony recognizing them becoming an adult. So a teenager would be considered an adult, at least in terms of their social status, and wouldn't necessarily need to have special attention drawn to that fact.
Younger than that, children generally weren't considered accountable for their actions. So a child wouldn't really be considered having a conversion and more just that they were raised in the Christian faith.
The closest we get is that of Timothy. Paul's first letter to him comments on his youth:
Don’t let anyone look down on you because you are young, but set an example for the believers in speech, in conduct, in love, in faith and in purity. –1 Timothy 4:12 (NIV)
Timothy's father was not a Jew and he was originally not circumcised until Paul convinced him to do it out of respect for some Jews they were going to preach to (Acts 16:1-6), so he definitely "converted" to the faith at a time when it was unclear whether circumcision was necessary to be a Christian.
However, Timothy is estimated to be about 48 years old at the time of the authorship of 1st Timothy. Granted, this is in relation to being a church elder, rather than a common believer, but it was unprecedented to have someone at that age having authority over so many in the early church.
Upvote:3
We do know of a youth ("νεανίας" in Greek, "adulescens" in Latin) called Eutichus who fell off the third floor window in Acts 20:9. He was a disciple of St. Paul, so presumably he or his parents had been converted previously.
9 And there sat in a window a certain young man named Eutychus, being fallen into a deep sleep: and as Paul was long preaching, he sunk down with sleep, and fell down from the third loft, and was taken up dead.
This is, of course, just to illustrate the point that the sacred authors did not think it relevant to stress whether any of the converts were young or old. We also know of the man who was healed by St. Peter in Acts 3:6–7, that in Acts 4:22 it is said:
22 For the man was above forty years old, on whom this miracle of healing was shewed.
Now, at that time, forty was quite old, and he was older than that when he became a disciple after being healed. However, it doesn't matter. His age is merely mentioned to reinforce the fact that the people of Jerusalem long knew him and knew that he was not faking either his disability or his cure.
So we can assume that, of the people who heard in Acts 4:4 of this miracle and became believers, there were indeed young and old men and women within that number — note, however, that the number of five thousand refers only to the number of men (ἀνδρῶν). The number of women and children was probably a like amount.
4 Howbeit many of them which heard the word believed; and the number of the men was about five thousand.