Lead the warm-up when the coach is running late. Nobody gave you permission, and nobody needed to.

Most authority in a group is not assigned, it gets assumed by whoever starts doing the useful thing. There is a gap in every room where somebody could begin and everybody waits to be told. Stepping into that gap is slightly uncomfortable and almost never objected to afterwards. Permission is mostly a thing people wait for rather than a thing that exists.

Next time the room is standing around, be the one who starts: call the first drill, open the discussion, set out the chairs. Keep it practical rather than bossy. Do it twice and you will notice how little resistance there was.