I remember a book, about fifty or so years ago that the Lost Army of Alexander the Great sailed from India to the Americas. This was not a claim by Joseph Smith who say Israelites did it.
I would buy a story about Hanno the Navigator discovering the Americas before any Chinese story.
LA Marzulli did a series of videos about the ancient Philistines packing up and moving to South America. A good portion of those alien elongated skulls they find in Peru supposedly have Middle Eastern mitochondrial DNA.
I think it is more likely that the lost armies of the Cartheginians fled to America after things went bad with the Romans. They may have traded there for centuries. Negro mercenaries were used by various Mediterranean civilizations. I would not be surprised if the Olmec heads were developed by negro soldiers who decided to stay and rule. I studied History and Appreciation of Art at university, and studied and traveled 2 summers in Mexico. A decade later I was at the Epcot Center in Orlando and saw an exhibit of Mexican pottery artifacts. I swear that one ancient cup had what appeared to be a Japanese style human figure on it.