1545 is well after European contact and close enough that it seems unlikely to be a coincidence. 1519–1521: Hernán Cortés conquers the Aztec Empire. 1532–1533: Francisco Pizarro conquers the Inca Empire.

Further low 10’s of millions of deaths on its own really doesn’t explain the 90% population drop across several hundred years here. Smallpox killed between 65% to 95% of Native American populations but it was far from alone. We’re talking devastating plague after plague for generations which canceled out the tendency for populations to rebound when competition is low. Something like 200+ million deaths on the conservative side over a few hundred years not just one or two devastating but short lived outbreaks.