Vaccines are developed not discovered,and you sure had smallpox vaccine in 1940.
Because they existed did not mean necessarily they were available, I didn't have one until 1948. Penicillin, was also in short supply, we had to use sulfa drugs, barely had either or Novocaine. Dentist charged 50 cents to pull a tooth, without Novocaine, or one dollar with. I remember that trip to the dentist very well, that was around 1946.
I broke my arm in 1944 and remember my mother and the Doc putting me to sleep with a tea strainer and a gauze patch, mom dripped the either out of the can by hand.