From what I understand, the smallpox vaccine was created without a working knowledge of diseases or germ theory. It was just guess work, observation, and deduction.
Edward Jenner saw that farmers living in close proximity to cows weren't dying of smallpox at nearly the same rate as others and thought their early exposure to the milder cowpox might be the reason. He extracted some puss from a cow's cowpox sore (gross) then made a small cut on a boy's arm and dumped the puss in (GROSS). My understanding is that people started coming around to his way of thinking after only a few of the subjects lived.
That's a pretty low bar, with no real technological entry fee. It would require a very specific set of circumstances, like saving the life of some young prince, but what happens if vaccine science is on its way when the Columbian Exchange begins?