3. Mexico’s History M exico's historical: Around 1000 BC, the first of Mexico's ancient civilizations, the Olmecs, established themselves in what are now the states of Veracruz and Tabasco. They worshipped a jaguar God, built cities, constructed massive stone head carvings, and spread throughout central and southern Mexico until their civilization mysteriously vanished around 400 BC. ancient ruins of the Olmecs, Maya, and Aztec is one of the most popular attractions in the world.