A bright light didn't suddenly flash above an engineer's head. And he didn't say "automatic transmission" and proceed to put one together.
Development of that most useful of automobile accouterments was a long, slow process, marked by many failures.
Contrary to popular belief, General Motors did not invent the automatic transmission. But GM definitely pioneered it and popularized it.
The principle dates back to 1904 and the Sturtevant brothers of Boston. It was a good idea whose time had not yet come. The 1934 Reo had a semiautomatic transmission, but the company was on its last legs and had neither the time nor the money to develop it.
GM had both the time and the money, and an automatic transmission was a pet project long before it saw the light of day in the 1940 Oldsmobile.
In My Years with General Motors, Alfred Sloan devotes considerable space to the corporation's work on transmissions. The quest for an automatic began in earnest in 1923 as an extension of many things that had been studied for years.