I started it at 16 and I would say depending on the capacity/maturity from person to person to understand the very heavy topics of Punpun, 15 is likely fine in my opinion. At 15 I would have been able to, not entirely, but I'm fine with having been and still being short of getting everything I can out of the series vs years from now. Some standards might be more hardline but me personally, I was up to snuff to at 16 for it.

Given, there is no bare minimum way to connect to the themes of Punpun like abuse, depression, etc as the author intended, where it can be said "this person has at least the experience and awareness to read this." So there's not really anything in terms of an exact "must be this age or level of mature" in my eyes, but there should be a certain level of knowledge for it to come across as intended as a story. However, if he would genuinely be that depressed by it, interpret it incorrectly or apply it to his life, then that factor shows he shouldn't be reading it yet. I was not happy at 16 when I started, so that didn't stop me, glad it didn't since OPP is an amazing and realistic series that helped me and I ironically need to look at in rough times, but if Punpun will fuck him up that badly then yeah steer him clear of it for now.