The first humans in the Americas encountered such now extinct animals as the giant sloth,

  the mammoth and sabre-toothed tigers.

There appears to have been successive waves of migrants into what is now Mexico starting in 50,000 B.C. at the beginning of the Pleistocene Ice Age . When the Earth turned warmer and the Bering Straight land bridge went underwater around 8,000 B.C. the migrations out of Siberia ceased .

Stages of Indian Development

Great Mural Rock Art , Baja Mexico

Some of the Rock Art painting in Baja date to 7,500 years ago

From 40,000 - 5,000 B.C. Pre-agricultural era, the people were nomadic hunters and food gatherers .The year from  5000 - 1500 B.C are called the Archaic  era. There were agricultural beginnings, small permanent villages .

From 1500 - 200 B.C.Pre-Classic era More elaborate settlements, ceramics.

From 200 B.C to 900 A.D.The Classic era of great Mexican civilizations, urban societies with priest rulers, monumental architecture .

900 A.D. - 1521, the Post Classic era, theocratic societies become ruled over by warriors, appearance of metallurgy, excess of human sacrifice.

an atl-atl

The early humans hunted animals spear throwers called atl-atl .Bones of  mammoths with stone points in their ribs have been found that are about 12,000 to 10,000 years old .Around 7500 B.C. the environment became drier and many of the huge animals hunted became extinct and the hunters turned to small game .Around this time the crude beginnings of agriculture began, with maize or corn being the most important crop .The earliest examples found are from 5000 B.C. at Tehuacan .Around 2000 B.C, the first pottery appears .

Around 1500 B.C. farming had enabled large population centers to be formed .Terracing and chinampas ( floating gardens, with mud piled on rafts ) begin to be seen. Clay figurines, usually of females are found in great numbers, possibly as fertility talismans .

Archaic inscriptions on rocks and rock walls all over northern Mexico (especially in the state of Nuevo León) demonstrate an early propensity for counting in Mexico. These very early and ancient count-markings were associated with astronomical events and underscore the influence that astronomical activities had upon Mexican natives, even before they possessed urbanization.

In fact, many of the later Mexican-based civilizations would all carefully build their cities and ceremonial centers according to specific astronomical events. Astronomy and the notion of human observation of celestial events would become central factors in the development of religious systems, writing systems, fine arts, and architecture.

The Olmecs 

Olmec 'wrestler' , basalt, found in Arroyo Sonso, Veracruz 1200-800BC

One of the first civilizations to emerge in Mexico was that of the Olmecs in rainy region of Tabasco and Veracruz .One of the dominant images from the Olmecs, is that of the were jaguars. The Olmecs believed, that at some distant time in the past, a woman had born children of a jaguar .

The Olmecs had hieroglyphs and a calendar and reached the height of their development between 700 and 400 B.C.As the first civilization in Mesoamerica, the Olmecs are credited, or speculatively credited, with many "firsts", including the Mesoamerican ballgame, bloodletting and perhaps human sacrifice, writing and epigraphy, and the invention of zero and the Mesoamerican calendar. Most of the Olmecs were maize farmers .

Olmec Altar, La Venta, with half human-juguar babies

The Olmec, whose name means "rubber people" in the Nahuatl language of the Aztecs , are strong candidates for originating the Mesoamerican ballgame so prevalent among later cultures of the region and used for recreational and religious purposes. Their political arrangements of strongly hierarchical city-states were repeated by nearly every other Mexican and Central American civilization that followed.

Olmec Head

One major site at  La Venta has a large pyramid and a population estimated to be 18,000 .The Olmecs were masters at carving jade and their most famous legacy are their huge stone heads, some of which are over 9 feet high and weigh up to 40 tons , wearing a sort of helmet . The best-recognized aspect of the Olmec civilization are the enormous helmeted heads. As no known pre-Columbian text explains these impressive monuments have been the subject of much speculation. Once theorized to be ballplayers, it is now generally accepted that these heads are portraits of rulers. The basalt from which the heads were made came from over 50 miles away and were dragged or floated on great rafts with what must have been a huge amount of human labor . They were made with stone tools .

Olmec altar or throne

The jaguar was important to the religion of the Olmecs, which seems to symbolize fertility and the god of rain .

                Olmec priests, possible mirrors on headbands

The Olmecs gradually declined, perhaps from pressures from the rising Maya and Teotihuacan civilizations .Around 900BC the great Olmec center of San Lorenzo was destroyed, from invasion or revolution. There is evidence of much violence as many monuments were destroyed . It is not known with any clarity what caused the eventual extinction of the Olmec culture. It is known that between 400 and 350 BC, population in the eastern half of the Olmec heartland dropped precipitously, and the area would remain sparsely inhabited until the 19th century. This depopulation was likely the result of environmental changes: perhaps the result of important rivers changing course or silting up due to agricultural practices.