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.
But surely they would reproduce? There is no genetic evidence of African genetics in south americans.
Also, there are no African skeletons found. But i admit it can be difficult to find a skeleton in a jungle.
It seems to me that it is very difficult for a foreigner to just come ashore and become leader of a people that don't even understand what the dude is saying, especially when those Olmecs already had leaders which controlled a vast army.
The tree-ring data worldwide recorded a severe event at 1159BC.
Troy was destroyed, the middle bronze age ended, there was the David plague and the Shang dynasty collapsed all about the same time according to Professor Mike Baillie.
We must have had a terrible volcano or a cosmic impact. Lot and lots of problems worldwide at that time probably driven by the event recorded by the tree-rings. The Chinese recorded that at the end of the Shang dynasy that "250,000 people, took to the sea."