Development gets done in whatever way makes best use of the available resources at the time. The overwhelming majority of the cities and towns in Europe were built out before transportation over land was slow and expensive so you had dense town centers surrounded by farmland and dense cities surrounded by even more farmland so to avoid spending precious resources on transportation. The practical limits on transportation constrained development.
By comparison huge portions of the US were built out after the advent the automobile (often tearing down and building over places that were previously more densely developed) and being geographically large there was always more land to build into so you got sprawling development because overcoming distance was fast and cheap.
The way we have more or less not built any infrastructure since the 20th century despite increasing population (and increasing clustering of the population in urban areas) is starting to catch up and incentive density but it will take time and policy sticks/carrots if you want it to happen faster than it organically would.
So yes, Europe to a large extent did win the lottery in that regard though they didn't know it at the time.