Foreigner opening a company in US
You can certainly register a U.S. company (either an LLC or a C-Corporation) without having a visa, or being a resident of the United States.
Registering a U.S. business may be done online, without having to provide a social security number or U.S. address. (You may use a home or business address abroad for the business address). Additionally, you will not be required to submit any financial or identification documents.
We have a research article titled 'U.S. Companies for Foreigners', which will guide you through the application process, as well as compare the different entity types you could register as well as a comparison of the top recommended states.