The article linked below on The Atlantic said:

Air-conditioning’s major public debut was at the 1939 World’s Fair. Carrier hosted the Carrier Igloo of Tomorrow expo, where 65,000 visitors would experience air-conditioning for the first time, boosting consumer interest. Over the next decade, as the air conditioner shrank in size, advertisements for the machine shifted their appeals from men in the workplace to women at home.

...

Basile points out another, less obvious move that increased the device’s popularity: In 1959, the U.S. Weather Bureau created its “discomfort index”—we know it today as the heat index, a measure of temperature and humidity combined. The discomfort index gave an unexpected boost to air-conditioning by, as Basile says in his book, putting “people in mind of cooled air.” Now the public could gauge if it was too hot to go outside. If they could afford it, there were plenty of air-conditioner manufacturers offering solace from the weather.

https://www.theatlantic.com/technology/archive/2017/08/the-moral-history-of-air-conditioning/536364/

Short answer: 1955-1970.

The breakthrough was the development of the window unit, first patented in 1932 but made much more practical in the 1940s by engineer Henry Galson. Sales of room air conditioner units first topped one million in 1953. By 1970, it was common for homes in the South to have at least one window unit, and new houses across the Sunbelt were being built with central units. In 1965, just 10 percent of U.S. homes had it; by 2007 the number was 86 percent.