Hi OP, we were new to the area when DS started school so I was really proactive in inviting loads of class friends over for playdates.
Thick skin, big smile, didn't care if I got blanked or refused, no hard feelings, just asked the next person on the list...
We also do a sports club where there are non-school friends, who I also invite over to ours, and chat to people in playgrounds/out and about, and I'm quick to swap numbers and follow up with an invite.
Every couple of months I'll invite a group over, parents and kids, so halloween, xmas time/new years, feb half term, Easter egg painting and hunting, etc etc.
We have made good friends this way by casting a wide net and not sweating when it doesn't work out - not a lot of pressure on one 'special' friendship, etc.
If any of that sounds possible for you then that's a good way to go. I agree that you being friendly and warm, but also resilient when a friendship fizzles out, is all good modelling for your DS.
Really hope things improve for him, best wishes.