I went to baby groups largely run by paid staff and it was the same for me.
I was lucky enough to have an easy birth and a "content" baby, so by week 3 I was eager to just get out of the god damn house and see people, anyone! Especially as I was taking time off from a very full on full time job. I felt claustrophobic and anxious with my summer born, to a point I would just invent housework to do, whilst baby happily slept!
I can only imagine that the groups I attended, my set of circumstances where probably not the intended target audience, in the nicest possible way.
A lot of the activities and clases they offered was around basic cooking, cleaning etc, on top of the "stay and plays" and there was a lot of struggling families that attended, lots with the supervision of social services. About 95% had older children too, and they wasn't allowed to bring them to groups, was on low income or didn't work, so I guessed they just didn't think the turn out was great so closed.
Despite, what appears above as a dim view of the groups, I throughly enjoyed the groups, and made life long friends with lots of the parents there.
We took up swimming, just ask your GP if you can go. I believe it's the mothers health not babies (despite popular believe re jabs) that matters, we was going as early as 6 weeks.
I also met up with the friends I met from the groups in coffee shops, parks, etc. And even created a walking group x