My general advice is that it can take time, years not months, to find a good fit with other parents. I've had trouble fitting in many times in my life and I now just take the long-range view - eventually you will find a likeminded tribe. I tend to try to break in by being helpful, which works, and then see who has common interests. Here are a couple of ideas that may or may not fit your style:
--This won't help you fit in, exactly, but -- as you say you are concerned about your kid being left out -- one option is to be the parent who lets your son invite a friend or two to whatever activity you are doing, like sledding, going to the park, the bakery, and when they are older places like SkyZone, the Lego store, pumpkin patch, berry picking, etc. Obviously covid will affect such plans now, but from my experience, parents who both work FT and who have multiple kids are more than happy to let their kids go on such playdates. I think this only works for people who aren't bothered by the lack of reciprocity and are ok with this financially; if this is you, it can be a way in to at least start talking to other parents and possibly developing a connection that might turn to friendship.
-- Another idea is through your kid's activities. For example, the parents of kids on sports teams, particularly travel teams, can become pretty close over the years and will start doing adult social things like happy hour and girls nights. If you go to these events, you will get along better with certain parents, and then can take baby steps towards friendship with them -- again, through actions, like offering to carpool, doing favors like lending extra shin guards, asking for and giving advice, group lunches during tournaments, volunteering to plan the end is season party with other parents.
Most importantly, be yourself-- this approach works for me but won't fit everyone. Good luck! You sound great and someone will be lucky to be your friend.