In addition to the main question, what was the legal age boys could join the army in nationally regulated armies such as during Roman times? Moving a bit forward in time, I'm aware that boys during the Medieval period were considered men at 12 and were required to go on manhunts when they were called for. Were they also allowed to join the English army at this age?
The issue with your question is, the answer varies geographically and with time. So maybe narrow down your search from "Roman times" to "late republic around 100 BC in rome?"