note this article claims the die-off happened years before the Mayflower/pilgrims came.
Yes, the spanish had been in the Americas since 1492, and the Pilgrims landed in 1620. That gives 128 years for the Old World diseases to sweep through. San Salvador probably didn’t have any locals left in very few years, and Cuba was cleared soon after. Cortez documented that he was aided by epidemics in his 1518 expedition, and Pizarro’s expedition benefited from an epidemic of bartonellosis in 1524.
The Pilgrims didn’t cause the epidemic, but the benefited from it.