Without understanding the full scope of your intended business, it’s hard for me to give a precise answer, but I will do my best.
Generally speaking, it’s very easy to register a company in the United States as a non-U.S. resident. You can apply online, and do not require filing personal, financial or identification documents to the state.
Opening a business bank account is difficult remotely, however, if you are able to cross the border to any state you can open a U.S. bank in-person in almost any bank, and it’s typically OK if the bank is located in a different state than the state of registration.
Other than that, depending on the state and type of entity, you may have annual obligations such as an Annual Report, Franchise Taxes, etc.