Good question. The nearest highlands to the American southwest are the Rocky Mountains.
They would have followed the high desert route, which would be the Chihuahua desert up into the Rio Grande valley. The southern extent of the Rockies are the Sangia de Christo Mts of northern New Mexico. There was extensive trade between different areas in Mexico and the Southwest, with some of the Spanish introduced European food crops actually arriving in New Mexico before the Spanish got here. It’s actually an unsurprising conclusion that the corn got here more than one way.