DD was in a hot shot group from when she was about 5 - and the girls she trained with from then on have remained her closest friends - her previous gym's HC was a big stickler about how the girls treated each other, and it was a relatively small program (maxed out with about 40 kids on team). She has had other girls she really bonded with over the years, but those girls are still her besties - which is a little hard because now at 12-14 yo, many of them have moved on from gym or not stayed together in training groups. The new (last summer) gym is twice as big and has a lot more teen and tween aged kids, so lots more drama...but after she left gym for 3 months she initially came back for the friends, but has stayed back in the gym because she wants to "finish what she started", and although she is still MUCH happier if she gets to train with a bestie, her BFF quit this week and she misses her, cried over it, but didn't spend a moment thinking about quitting too. (I was half sure she would). So, long story short, even the girls end up being there for themselves and not the friends as they hit levels 8-10.
For my boys its been much different - we also homeschool, but I am sure that because they all do gym semi-together, the need for friends at gym is less so. (In fact part of why DD went back and fought to get through so much last year was she liked being a gymnast with her bros...) For my oldest who started competitive gym at almost 11, he had "gym friendly acquaintances" from the first comp season but only real friends I'd say this last 18 months. And yes they do hang out outside of gym about 2 times per year, and text perhaps 5 texts to DDs 97,000....but they are true "guy friends". My younger boy started having real gym friends at about age 8 I'd say. He does do more outside of gym with them - they like to go to open gym together where they mostly mess around making forts, etc. He started competing L4 at age 6, so I'd say it took a couple years...
Also, in retrospect, I think for my boys and the boys I know outside of my family (I'm a peds doc), boys don't make close friends young like girls do - in general.
I do think that competing really helps them make friends and I still like it when our team does little meets where several levels can compete together (not just because then there's a chance I don't have to sit through 2 whole sessions) because they support each other and we usually try to go out to lunch or dinner as a team before our 3-6 drive back to our little town. Your boy started right in the middle - when school starts my guess is some new boys will come and some will go - lower level boys gym is very fluid and laid back, so we've experienced more coming and going than with DD - where the little ones were super into it ready to go to the Olympics tomorrow - until it got hard or they found other things...
I'd see if there is a chance to do more open gym type play with the other boys, but I'd also give it time and let boys be boys...