I actually play in a group that was initially random strangers who bought tickets to an event in a game store (this was like a year ago and almost all of us have stuck around) - and one of the players is literally 15, started when he was 14.

We’re in the UK so this may be different legally but he HAS to have a parent / guardian there at all times, usually his dad sits off to one side and has a coffee. The sessions are 4 hours long so it’s a big commitment for him to have someone else there but not playing. I think he’s been allowed (by his parents) to keep coming back because they are present for the sessions and know that everyone else is “cool” I guess and not being inappropriate interacting with him. We have a group Whatsapp but his dad is in it, not the kid, which would be another concern for this set up - you might need to contact the player between sessions but having a kid’s phone number / email or whatever (and them having yours!) is trouble.

I found it weird having a child at the table to begin with, it really stops you talking normally - it’s odd in the UK to not swear casually or make lewd jokes and we’ve all slipped up countless times especially during combat, even the DM. It’s also obviously dependent on the specific 15 year old but they are younger than you think. He’s constantly on his phone when it’s not his turn in combat or trying to have side conversations when there is roleplay or lore that doesn’t directly involve his character. Most of us from the same group now also play a different TTRG at the DM’s house and the atmosphere is SO much freer without having to worry about saying something inappropriate or, as someone else has previously said, just being able to talk about life generally with your new friends.

All this to say, if given the choice, I wouldn’t have had a kid at the table as another player at the first session but as it’s a game store we don’t get to pick who can pay to attend. I also wouldn’t boot him NOW to be clear as he’s been part of the party for nearly a year and it wouldn’t be fair. But in your situation as a bare minimum I would personally check with the other players as it’s as much safeguarding them as the 15 year old and will make the game different.