You put the trains where the people are, not in the middle of vast unpopulated stretches. Comparing land area is misleading and unhelpful.

Yeah thats a useful factor for all those "visiting mom in Portland" trips from Washington DC that a train is obviously meant to replace, not any of those "100 mi or less visits to mom" that de facto MUST be taken in a car regardless of the population density of the surrounding 100mi radius.

Also we should ignore the fact that the US already had a national rail network and STILL DOES for freight and had frequent regional rail service to even incredibly small podunk nowhere towns for decades. It's clearly impossible! We're too big! IT CAN'T BE DONE!

The vast size of the country sounds like an argument for trains, rather than against it? Trains are a comparatively cheap way to provide fast transportation between places where people actually live.

Now do China.