To quickly sum up, the Maya were first but learned a lot from the Olmecs, who started 1,200 years later.
What did the Mayans and Olmecs have in common?
Many matured into advanced pre-Columbian Mesoamerican civilizations such as the: Olmec, Izapa, Teotihuacan, Maya, Zapotec, Mixtec, Huastec, Purépecha, Totonac, Toltec, and Aztec, which flourished for nearly 4,000 years before the first contact with Europeans.
The Olmecs, regarded as America’s first civilization, existed from about 1500 to 400 BC. They resided in what is known as “Olman”, or the Olmec heartland, situated in Mexico on the southern tip of the Gulf of Mexico.
The Maya developed their first civilization in the Preclassic period. Scholars continue to discuss when this era of Maya civilization began. Maya occupation at Cuello (modern-day Belize) has been carbon dated to around 2600 BC.
Some historians assert that the Mayans were the descendants of the Olmecs.
The Olmec were American Indians, not Negroes (as Melgar had thought) or Nordic supermen.”
The Maya were native people of Mexico and Central America, while the Aztec covered most of northern Mesoamerica between c. 1345 and 1521 CE, whereas Inca flourished in ancient Peru between c. 1400 and 1533 CE and extended across western South America.
Olmec civilization arose along the Gulf Coast of southern Mexico about 1200 B.C., in an area that the Aztecs later called Olman, “The Rubber Country.” There, quick streams flowed into large rivers, with easily cultivated soil and bountiful forests providing sustenance.
The End of the Olmec Civilization Around 400 B.C. La Venta went into decline and was eventually abandoned altogether. With the fall of La Venta came the end of classic Olmec culture. Although the descendants of the Olmecs still lived in the region, the culture itself vanished.
Olmec, the first elaborate pre-Columbian civilization of Mesoamerica ( c. 1200–400 bce ) and one that is thought to have set many of the fundamental patterns evinced by later American Indian cultures of Mexico and Central America, notably the Maya and the Aztec.
The Maya are probably the best-known of the classical civilizations of Mesoamerica. Originating in the Yucatán around 2600 B.C., they rose to prominence around A.D. 250 in present-day southern Mexico, Guatemala, northern Belize and western Honduras.
The Olmecs studied astronomy and developed a system of writing and mathematics. They were the first Mesoamerican culture to build pyramids. Their calendar and religious beliefs appear to have influenced later cultures. In fact, many scholars call the Olmecs the “mother culture” of Mesoamerica.
Maya pyramids The Maya are a people of southern Mexico and northern Central America (Guatemala, Belize, western Honduras, and El Salvador). Archaeological evidence shows that by the Preclassic Maya ( 1000 B.C., approximately 3,000 years ago ) they were building pyramidal-plaza ceremonial architecture.
Drought theory. The drought theory holds that rapid climate change in the form of severe drought (a megadrought) brought about the Classic Maya collapse. Paleoclimatologists have discovered abundant evidence that prolonged droughts occurred in the Yucatán Peninsula and Petén Basin areas during the Terminal Classic.
The positioning of some South American and North American reference populations near the compact Mayan cluster suggests phylogenetic relationships among these Native American groups and Mayans likely due to sharing an Asian common ancestry.