I have read that Olmec could be from China. Many of their artwork and writing looks Chinese. I would not be surprised if Shang Dynasty had Black emperors. If I recall, I read there were Blacks living in China. I have seen those Olmec head statues before and they look like Blacks.
Australian Aborigines
When at the Epcot center in Orlando (Disney) I saw a Mexican cup that had figures that look exactly like Chinese art I had studied about in college.
I think it is entirely likely that a significant influence came from the Orient. The Aztecs, johnny-come-latelies from the north as far as southwestern USA, claimed ancestors from a great lagoon to the west (I think they called this Atlan or Atzlan). If the Chinese landed there it could have been the great mythic source of culture.
I also think some influence came from the Mediterranean/North Africa. The 12th Century BC was a time of great upheaval in the Med. The Mycenean civilization of the Greeks collapsed. A somewhat mysterious group known as the Sea People gained sea power and conquered various regions around the Med. I think they were Phoenecians, or eventually acquired that name. At that period Negro mercenaries were used aboard ships as fighting men. Also this was a period of time when huge statues of rulers were being carved along the Nile.
My conjecture is that one or more ships of the Sea People, with Negro mercenaries aboard traveled to the Olmec coast. Perhaps they had to escape trouble at home. Perhaps they were stranded. I imagine one or more of the powerful Black mercenaries taking up the reins of power. They would have been illiterate in all likelihood. They might have wanted great statues like the ones in Egypt to record them for posterity. They might have settled for giant heads as the most important part of the representation. That's my theory.