My daughter has slept on her tummy since the night she came home from the hospital. And to this day (she is almost 2) she will not sleep any other way.
I think the main concern would be if he were to put his face down into the mattress, it could compromise his breathing.
A good way to check would be to put something on his face, with your supervision of course, while he is sleeping on his tummy. Like a blanket, or a toy. If he can move his head away, or pick up his head and rotate it, its a good indication that he is strong enough to sleep on his tummy.
Another thing to consider would be the risk of SIDS. Do you smoke? Did you smoke when you were pregnant? Is he nursing? Was he a preemie?
Follow his clues, and your instincts.
Best of Luck!!