What car had the first automatic transmission?

Oldsmobile offered the first fully-automatic transmission, called
the Hydra-Matic, in 1937. The transmission used four speeds and
added fifty-seven dollars to the price tag of the car.

By the late forties and fifties, the Hydra-Matic was also used by
Cadillac and Pontiac, as well as by independent automakers such
as Nash, Hudson, and Kaiser-Frazier.