It sounds like he doesn't like lying flat. Is it possible that he has reflux? Otherwise it might just me something that he needs to get used to. I would just try it every day. Give him a minute and if he doesn't stop crying pick him up again. Try and get him used to it, but don't force it. It won't hurt him not to spend time on the mat yet if he doesn't want to. The daily tummy time is important though, so do this every day, just for a short time to start, and you can stay with him if he gets upset.

Things get easier as the bubs get bigger and more used to this world, and as we get used to being parents.