M.O.
3 months is really too young for "progress." The point of tummy time at this age is to get him comfortable in this position, so he can start to be mobile between 5 and 8 months. If anything, use tummy time as social time. Lie down face-to-face and silly-talk to him. Have his toys "wave" to him. But don't expect anything FROM him for another 2-5 months at least.
He'll only get to be a teeny-tiny infant once. Let him have that time. The next phase -- when he's mobile, when you have to childproof everything, when he's putting anything and everything in his mouth -- that'll come in due time. No point, and no value, in rushing it.