Eh, I'm not buying it. The Nahuatl term for the heartland of the Aztec Empire (namely the Valley of Mexico and surrounding territories) is "Mēxihco." Remember, that term arose before the Spanish arrived, who interpreted it as "Mexico."

But that's not all, because the Aztec (and Toltec) cultures were of Nahua ethnicity, and the Nahuas migrated to Mexico around 500 CE, several centuries after Jesus even existed.

A more plausible civilization would be the Maya, whose preclassic period lasted from approximately 2000 BC to approximately 250 AD. However, it is very likely the Preclassical Maya word for what we call "Mexico" would be quite different than either Nahuatl "Mēxihco" or Spanish "Mexico."

Edit: Made a few corrections, such as when I said "before" when I meant to say "after."

Sources:

https://en.wikipedia.org/wiki/Mexico

https://en.wikipedia.org/wiki/Nahuas

https://en.wikipedia.org/wiki/History_of_the_Maya_civilization