Not really possible without ASBs under the conditions of the challenge: you've already insisted that the US states keep their present population, which takes nuclear war off the table. In order for this to work, then, you need to add over 37 million people to the US population, and then provide a sane reason for them to go to Wyoming, which is...unlikely.
You could make America a very nasty place to live (KKK-run government, fascism, etc) and have a racist government move all non-whites into Wyoming, turning the state into one big area filled with concentration camps; that's a stretch, but it's the best I can think of. Explain away the addition of 37 million Americans by keeping abortion illegal, as well as slowing the introduction of contraceptives.