All the things attributed to the American car-centric lifestyle were a thing to some degree everywhere. Then people got tired of it and changed it. Probably Europe not having much petrol also helped, which also explains the tendency of the European cars having significantly smaller and efficient engines.
There are plenty of cool videos of European cities that used to be traffic hells that turned into bicycle friendly walkable places. Though admittedly the hell part still exist for those who choose the to drive the cars.
That said, like you mentioned: that didn't stop them from making traffic hellholes. Designing a city to need cars is a choice.
Cars are a huge problem in Europe as well.
Take Mainz, Germany; where my father is from; the core of the city is a walkable old city (which my Opa knew every corner of having worked for the city for decades, and he toured me around all over it when I visited...). But then around it are a whole bunch of villages which grew into suburbs, and are connected by freeway. But it seems to me that because each of those villages, towns, and the central city already had a tradition of walkability, the connectivity between the towns, villages, suburbs took that into account when the post-WWII reconstruction happened.
In Mainz I was able to take a streetcar out from the centre of town to a small village in under 45 minutes and go walk in a forest. Here in southern Ontario -- where we have similar density and population to the Frankfurt/Rhine corridor -- such a thing requires a car.