You must move to Mexico with your spouse and live there for two years with an immigrant visa, then you can apply for Mexican citizenship. You can have both a Mexican and a US passport and be a dual citizen. If you were not married to a Mexican citizen, you would have to live there for four years.
If the question is asking when the first Mexican Americans came to the US, they didn't. The US came to them. They were alreaday living in Texas and the Southwest when these lands became part of the US in the 1840's.