What about movable type could not have been made centuries earlier? Was there some new technology that would have made a printing press impossible before then, or was it simply that nobody had ever had the idea?
It wasn't so much the press itself that was the problem--it was the ink. They needed ink that would have the right consistency, be smooth enough to be picked up by the type and dry quickly on the paper before it could smudge, while still staying wet enough to keep working for each subsequent copy of the page.