It may be hard for people in many places to grasp, but even in eastern states there are many, many areas where you could pick a direction and walk many miles without seeing anyone.
Below a certain population density (likely in the hundreds to low thousands per square mile), public transportation simply is not feasible.
Most major American cities that existed before the car still have public transportation. NYC is a prime example of somewhere you can live without a car. Most other cities still have functioning bus systems, though not great.
It's the suburbs where you really need a car, and the development of suburbs was spurred in large part by the car. So you have your historical order wrong.
But mostly it’s the suburbs and small towns where cars are totally necessary. Those areas were settled less densely because everyone already had a car. They never had subways and bus routes.
Are there any first world cities that substantially grew in area since 1920 that aren’t primary automotive cities?
Firstly, the US is different from many parts of the world. Not only it's massive, but swaths of American urbanization are shaped around cars as a basic necessity, especially with the adoption of suburbs. Most of the US outside of big cities are car-first towns both in infrastructure, planning, and services.
In turn, having a car for many Americans is more than an efficient way to get around, it is the only way to move safely and reliably.
Many parts of the US have no public transportation, no reliable ride-sharing, no safe way to bike (both the roads and the culture are hostile towards cyclists).
For more information, I'd suggest reading on the phenomena called "Automotive city" https://en.wikipedia.org/wiki/Automotive_city