could be weather events. Consider the NC/SC storm surge. Flooding in Texas, tornados, volcanos from NM to the Pacific.
Or could be virus: European settlers to the Americas caught Hemorragic fever. The Indians also suffered from it; some populations may have built some level of herd immunity over time and some not. Carried by varieties of mice/rats drawn to subsistence farms/homes. Or, maybe some other virus/carrier. T-rex?
http://www.infectionlandscapes.org/2013/02/american-hemorrhagic-fevers.html
and,
“the epidemic of 1576 which killed 45% of the entire population of Mexico”
I can’t imagine any terrestrial weather event that would wipe out every human in North and South America, from the highest Mountain to the deepest valley, from the most arid desert to the wettest rainforest, from the tundra to the equator.
I have trouble imagining an epidemic with 100% fatalities, not missing a single isolated village.
Where the the older civilizations go?
I recently saw the proposition that something like 20,000,000 people were in North America before 1492, and most of then died subsequently from diseases brought from Europe/Asia. Europeans had been winnowed for millenia by diseases carried west from Asia. NA did not have that degree of disease spread and survivors immunity and was much more vulnerable.
We should check the DNA of Cherokees and coastal Mexican Indians to see if there is some residual European DNA. Of course after 6 generations you are down to 1/1000th trace of one ancestor’s DNA, so it will be hard to find. If I remember correctly, the first Spaniard to travel down the Amazon from the Andes was surprised to discover some white people among the population. It also would appear that the large settlements he saw were pretty much wiped out after he passed through. Probably disease.