S.B.
He's only 10 weeks old. I don't know that he should necessarily be "pushing" himself up yet.
Lots of babies get frustrated with tummy time. If they are used to being on their backs, being on the tummy is a whole different perspective on the world. Until they figure out how to lift or roll over, it can be frustrating.
Let him grip your fingers. Give him different toys and textures to explore and grab. Bend and raise his little arms while he's on his back after bath time or diaper change. Just play with your baby.
I wouldn't be overly concerned about this just yet. He's still pretty new.
Not all babies get things figured out at the same times.
He should have a well-baby check up soon, right? I would bring it up then. If all other exams have been fine and they didn't detect any issues with muscle tone, etc, I wouldn't needlessly worry. You can always make an appointment sooner if it will make you feel better and ease your mind.
There's never any harm in that.
Best wishes.