It sounds like he wasn't even the first among his contemporaries.

But it is known for certain that in the years following 1770, at least six people in England and Germany (Sevel, Jensen, Jesty 1774, Rendall, Plett 1791) tested successfully the possibility of using the cowpox vaccine as an immunization for smallpox in humans.

https://en.wikipedia.org/wiki/Smallpox_vaccine#Early_vaccina...

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2279376/