non residents can open company in most if not all states. once entity is created - anyone can fund it. you just can't be hired by this company and be US residen

non residents can open company in most if not all states. once entity is created - anyone can fund it. you just can't be hired by this company and be US resident in the same time. But you can be on US territory to sign contracts, or you can work for company while being out of US land. but after going through work visa i can say it's doable, but really complex if you are not from "good" country, like canada, australia, etc. =)