That's not what we were taught.

You do not realize just how old the three other older professions are... For the sake of brevity, the 2nd and 3rd are politics and religion... (religion being a tool of politicians determines the order)

but maybe they found that powdered bitumen and whatever they mixed it with would kill infection--or slow it down so the poor bastard with the bad tooth didn't die of sepsis.

I've seen some of the old bones that didn't get this done, holes in the mandible or maxilla showing where tooth abscesses ruptured through the bone before they turned fatal.

Dentistry and dental anesthesia are things I hope we can save come the Apocalypse.

I googled bitumen and it said this:

{DEFINITION of 'Bitumen'
A substance produced through the distillation of crude oil and known for its waterproofing and adhesive properties. Bitumen production through distillation removes lighter crude oil components, such as gasoline and diesel, leaving the “heavier” bitumen behind. It is often refined several times in order to improve its grade.

BREAKING DOWN 'Bitumen'
In modern times bitumen is most likely to be manufactured from crude oil, but bitumen can be found in nature. Deposits of naturally occurring bitumen can be found at the bottom of ancient lakes, where prehistoric organisms have since decayed and have been subjected to heat and pressure.

Bitumen is generally for industry use. Early uses of bitumen involved its natural adhesive and waterproofing characteristics, but it was also used as a medicine. It was used to bind building materials together, as well as to line the bottoms of ships. Herodotus, a fifth century BC Greek historian, claimed that the walls of ancient Babylon were strengthened through the use of bitumen. The material was traded between ancient civilizations.}

My question is this- Where do you think they found the stuff & how would they get it not to dissolve in the tooth?

Asphaltum and crude bitumen are waterproof, and were one of the first 'super glue epoxies' know to man. I suspect the dentist was an arrow or spear maker because the tar adhesives were used extensively to fix points to shafts.