The leading theory currently is that the primary wave of migration into the Americas began in the vicinity of Beringia, the landmass linking easternmost Siberia to Alaska when sea levels were lower during the last glaciation (map). This early migration most likely traveled down the Pacific coast, rather than travelling overland, reaching southern Chile by 18,500 years ago. Some of the various coastal communities founded by the initial wave of migration would have then spread inland independently from one another, merging and diverging as they went to form new groups. By 16,000 years ago, if not considerably earlier (possibly 19,000 years ago), they had reached the east coast of North America. Later migrations into the continent could have used an overland route once the glaciers covering much of Canada began to melt; this is the Ice-Free Corridor model which was once the dominant model for the peopling of the Americas, but as we learned that there were people here before the ice melted that fell out of favor.
It's from these early Paleoindian groups that all later Native American nations descend. Mesoamerican societies had little to do with the development of throughout the rest of the Americas. The Maya traded with people in the Caribbean. The Caribbean traded with people in Florida and northern South America. People in South America brought certain metallurgical techniques north to Mesoameica. Mesoamerican crops went north into what's now the US. Turquoise from the American Southwest went south to Mesoamerica. And so on. But Mesoamerican civilizations were in no way the originators for these other societies.