This is false. Europe always had public transit, up-front. If you look at e.g. Paris you see that the peak in car ownership and beginning of the decline coincides with the economic crash of 2008:
https://www.ceicdata.com/en/france/motor-vehicle-ownership-p...
Overall, the change has been small, and most people still have a car. And the metro network was very advanced by 1939 (unlike some US cities, these lines stayed):
https://en.wikipedia.org/wiki/Paris_M%C3%A9tro#/media/File:M...
That's in one of the densest and most famously walkable cities in the world. Most cities in the United States aren't going to be Paris anytime soon, and that's before we consider the dismal state of regional transport (particularly around the West Coast) which was also already extensive in France prior to 2000.
There is just no real basis for claiming that Europe restricted cars prior to building good transit. You might find it in one or two cities, but certainly not most -- in Europe, socialist and communist parties held significant sway until the late '70s in many countries (in a few they've hung on), and pushed for transit the whole time.