As with all other civilizations on Earth, the Mayan started out as nomadic people without a true cultural identity until they developed agriculture. In that part of the world, it was maize and beans that gave the hunters and gatherers the opportunity to put down roots and establish a stationary home. They also domesticated dogs and the large turkeys native to Mesoamerica that provided a considerable food source. These first villages began around 2000 BCE.
This was very near the time when the Olmec civilization came into being. Now, historians and archaeologists frequently express the idea that the Olmec were the original Mesoamerican civilization at the time. While this is generally true, they did not exist for an exceptionally long. As a structured society before the Aztec and Maya came along. They were, however, truly the first to create organized cities, cut stone for building purposes, and develop trade routes.
The next iteration of Mayan people was part of the Zapotec kingdom. They garnered ideas directly from the Olmec including ones about culture, religion, astronomy, keeping track of the days using a calendar, and writing. It is interesting to note that while the Olmec did not have a precise language, they did have pictorial codes to record certain things. The archaeological record for them is quite slim. The Maya, however, have quite a rich written history for those with the skills to figure out what their symbols mean.