There were absolutely massive die-offs of pre-Columbian populations across the Americas with as much as a 90% reduction in population before they bottomed out and started to recover. A lot of the history of the Americans makes a lot more sense if you imagine it as a post-Apocalyptic scenario. This didn't all happen at once of course and it took a very long time for populations to reach their nadir.

However what is Mexico had a few things going for it that what is now the US didn't.

More people: if you lose 90% of your population it helps a lot if you start with more people. Mexico has (VERY roughly) around 30 million people in 1492 while what is now the US had (again VERY roughly) a much smaller population of 4 million or so.

Earlier contact: all of this started earlier in Mexico so more time to bounce back.

More thorough contact: diseases spread all across Mexico much faster than it took to spread all across what's now the USA so you don't have new population continually getting slaughtered by disease etc.

Also the male to female ratio of European colonists varied from place to place with New England being closer to parity and Brazil being almost all male with a lot of points along that line. Overall, Mexico had a much lower percentage of female colonists than what's now the US, although that varied from place to place.

Source for pre-Columbian population counts which is a VERY contentious issue in academia and wide ranges in population estimates: https://www.sciencedirect.com/science/article/pii/S0277379118307261#appsec1

But it's certain that the die-off was massive. So massive that it seems to have caused some global cooling.