While automobiles existed earlier, mass production techniques pioneered by Henry Ford (starting with the Model T in 1908) drastically lowered prices, making car ownership attainable for a larger segment of the population. By the 1920s, significant improvements in road infrastructure and a burgeoning economy further accelerated the adoption of automobiles.
So, while some owned cars before then, it wasn't until this period that car ownership transitioned from a luxury to a more commonplace means of transportation for many Americans.