This has been run through many times, and I even made an abortive timeline on the basic premise when I was a misguided teenager. It is almost a cliche.
People bring up the idea that the Chinese didn't colonize much outside of China. Which is somewhat true, but misses the fact that most areas of present-day China are the result of a very successful colonization program by the Han people. Also disregards the unofficial colonization of Han populations into much of South-east Asia.
That said, there are a number of major issues that must be overcome.
The first is simply the fact that the Pacific is much, much wider than the Atlantic, and while the prevailing winds mean that any significant ocean-going in the Atlantic is going to yield the New World eventually, this is not true for the Pacific. Coast-hugging ships were pretty much sufficient for Pacific-Indian ocean trade thanks to the regular monsoons. The Chinese had little reason to sail off into the eastern ocean, unless they wanted to find Penglai or something, and little chance of reaching the New World and returning. I could see a purely exploratory expedition sent by an early Ming emperor, perhaps, but they'd be more likely to disappear or mayyybe reach Hawaii, extract some tribute from the locals, and turn back calling it success.
The second is the lack of any real reason for the Ming to colonize the New World, when there were areas much closer to home that were underpopulated and ripe for exploitation. The west coast has nothing much to offer the Chinese as it is.
I don't think it is completely impossible, just unlikely. If there were a set of circumstances in which the Ming became aware of an underpopulated continent in the far, far East, there still wouldn't be much impetus to go and colonize the area. Any Chinese movement to the New World would have to be non-government, probably merchants.
Say a Zheng He-style explorer in an ocean-going fleet was sent west, did manage to survive the Pacific crossing, managing to travel far enough down the coast to reach settled Mesoamerican peoples, and then get back, then maybe there might be some interest (gold!, after all, and unique trade goods). But it wouldn't be anything like the Europeans in the New World. No Ming conquistadors. Imperially-sanctioned high-risk, high-return treasure ship crossings exchanging bulk Chinese manufactures for gold and local goods? Maybe.
This would mean that some Eurasian diseases would probably be transmitted, particularly if the Ming merchants decided to see pigs, cows, horses and other livestock to the locals. This would mean a downturn in trade, but probably wouldn't be accompanied by Ming adventurers. So, when the Europeans arrived, they might be faced with a smaller native population, but one that is more immune to Eurasian disease, and access to livestock and some imported Chinese weapons and tools.