Hi OP, very much sympathise with your post - in similar version of the situation.
I'd suggest;
Write down on paper or block off on your online calendar, what time you actually DO have available. You sound to be quite busy already with the job demands etc. Then this makes it much clearer visually what availability you could have as a starting point, for where you are now in your life. E.g. if you know that weekday evenings are absolutely no good because right now, for now at least, you have to work late Mon - Thurs, then there's no point wasting time on looking at groups which only occur on a weekday evening. (I've personally found this can be the problem with Meetup groups).
Out of the (probably small) amount of time when you do have availability -what would you like to do with it that would benefit you personally ?
I also think it can be helpful to think of the situation as "for now", e.g. "I am really tied up with work / other items for now, but I can see that in xx weeks / months / years I would certainly have more time on a Monday evening and could then join xx group".
From my own point of view, it's totally pointless to recommend churches to you when you aren't religious, and I've personally never made any friends / social contacts through any gym /exercise group at all - I went to a yoga group for years, no one spoke to each other, just turn up and get on the mat in silence.
So for your situation - what kind of friend / contact would you like, as in- what would you imagine enjoying doing with this friend ? Then could that lead you to work out - what would be a "one step forward" strategy for now, even if it's not perfect ?