No, I'm pretty sure it's not the size. If I take my car and drive from Lisbon all the way to Moscow, that's about the same as going from NYC to LA in terms of distance.

I'll grant that it might be related to "free land" though, as I think it's mostly a matter of organization. But first there's this "single use" zoning mentality in the US, which forces people to travel for everything by design - in Europe ground floors were traditionally businesses, and upper floors housing - mix is the norm, cars didn't exist back in the day and people still had to get to things. Then there's the way cities grow - most places in Europe you can't just build swaths of single-family houses in the periphery of existing cities, either because it's already reserved land (parks/ecological reserve/farming/other uses) and because the access would be awful (already crowded highways) - so instead usually it's the existing town centers that already have good mass-transit connections (train, subway, ..) that see an increase in density: old single-family houses give way to apartment buildings or mixed use buildings (commerce, offices). So it kinda grows in "nodes", not as an ever expanding ring of single-family houses.

But this is simply a mater of policy - build a train line that connects a few several small towns in the outskirts, connect that up to some mass transit inside the city proper (subway ideally, if it exists) and boom, the density in those small towns that now have a good connection will skyrocket.