What evidence physical and religious would prove a relationship between the Mayas and other cultures from other places?

Until the early 1900's, the Maya civilization was considered to be the parent culture in Mesoamerica from which all other societies sprouted. There have been many Mayan sculptures and carvings found in the region, so all other carvings were also considered to be that of the Maya. One difference in the carving is that some carvings of large heads had faces with more African looking features than many of the other Mayan works. There was also evidence of a half-jaguar half-man beast, which also did not fit in with other Mayan finds. It wasn't until 1929, when Marshall H Saville, the Director of the Museum of American Indian in New York, classified these new works as an entirely new culture not of Mayan heritage. He named this culture Olmec, which means the "rubber people" in Nahuatl, the language of the Mexica ("Aztec") people. It was the Aztec name for the people who lived in this area at the much later time of Aztec dominance. Ancient Mesoamericans, spanning from ancient Olmecs to Aztecs, extracted latex from Castilla elastica, a type of rubber tree in the area. The juice of a local vine, Ipomoea alba, was then mixed with this latex to create rubber as early as 1600 BC.

It is not known what name the ancient Olmec used for themselves. Later Mesoamerican accounts seem to refer to the ancient Olmec as "Tamoanchan".