Native American Culture in New Mexico. â...Explore the rich history of New Mexico's Native American culture by visiting these monuments.â. There is evidence that Native Americans have inhabited New Mexico for over 2,500 years.Early ancestral Indians lived for centuries as hunter-gatherers throughout the Southwest.xplore the rich history of New Mexico's Native American culture by visiting these monuments, parks and sites. Aztec Ruins National Monument. Aztec, NM. The Aztec Ruins National Monument in northwest New Mexico preserves structures and artifacts of Ancestral Pueblo people from the 1100s through 1200s.