first probably 50 pitches. These circumstances assume the pitcher is throwing hittable balls - meaning strikes, or close to strikes, and you are swinging at every pitch, because there is no penalty for missing. I really don't think it would be that hard for anyone with decent coordination to put the bat on the ball as a result of that coordination and luck.
Now - If the question is - You get called up to the big leagues, how many at bats in a game where balls and strikes matter will it take you to get a hit, then the answer to that is going to likely be somewhere between hundreds of at bats to never because you quit trying from tennis elbow.