The alleged map from Zheng He's expedition includes the Gulf of Mexico, and the eastern seaboard. Supposedly, they explored the Americas on both the Atlantic and Pacific sides. From the part of the expedition that actually was documented, it would have been closer for them to hit the eastern side of N & S America than the western side. They went all the way to SE Africa.
Around the horn and across the Atlantic would be a more logical route than clear back across the Pacific. That expedition was very well documented. There is no mention of them ever going around the horn, let alone crossing either ocean.
There are even some serious questions as to whether a 450' wooden ship could even survive anything other than coastal waters. With a wooden ship, bigger=better only works up to a certain point. 450' is beyond that point. Big water would have beaten them to pieces.
The North Atlantic especially.
The whole Ming fleet story is absolutely fascinating. Points out perhaps better than anything else the differences between Chinese and European cultures, and why Western civ came to dominate the world.
Of course, we may be in the early stages of the process of surrendering everything we've built back to the barbarians.