K.M.
I did a tumbling class with my kiddo years ago with joco parks and rec. We had a good experience. Let the instructor take over and let yourself have a rest! Sit back and just watch. Most of the moms there were pretty friendly. Don't hesistate to start a conversation with a simple "which one is yours?" or "have you done this class before?".
Simple starters like this can lead to lasting friendships. I joined a playgroup through people I met at Gymboree and even though we have gone our separate ways, we still keep in contact through Xmas cards and the occasional get together.
As Barbara posted, comfy clothes are fine. I would bring along a pair of sweats (Hanes, very cheap at Walmart or Target) in case it is drafty or cool in the facility. As he gets more active and starts to warm up, you can take them off.
Have fun and hopefully you will meet some new friends!