Company formation and stay
You can register a business in the United States without having to be physically present. You are not required to have a social security number or a U.S. address, and you are not required to submit any financial or identification documents.
We have a research article titled 'U.S. Companies for Foreigners', which you will find helpful in guiding you through the different entity types and recommended states to incorporate in, as well as links to the applications where you may apply directly online.
Regarding coming to the U.S. to live, that is something you will need to consult with a licenses immigration attorney.