How to finish concrete ceiling - beam span calculation

I have a room below my garage (suspended slab). I want to finish the room/ceiling. The room’s dimensions are approximately 24′ x 23.5′ (this is to the walls, which are already framed/dry-walled). I don’t know if I can drill into the concrete ceiling, and would prefer to avoid that if at all possible. I would like to do 2 inches of closed cell spray foam insulation. What I’m hoping to be able to do is span the 24′ length with 2-4 beams, then anchor 2x4s perpendicular to the beams to create a suitable backing for something like drywall or another lightweight finish (lightweight shiplap, etc). How do I calculate a beam size that only carries its own weight, plus the weight of the ceiling materials? Height is a concern, it is a pretty low ceiling. I really only have about 9″ (7 after the spray foam insulation) to work with since that is the top of the entrance/doorway.

I may need to hire out an engineer, but I figure its worth a shot asking here first for ideas.

Thanks.