If you are determined to do business in the US, it will be easiest to do so while you are here. You won’t be able to open a bank account without the personal presence of a company representative.
To connect various payment gateways and services from PayPal to Braintree and Stripe, you will need a tax identification number (EIN, employer identification number), bank account information, and an address in the US.
Otherwise, there is nothing complicated. In my companies, I accepted payments to a bank account, and by check, and through PayPal, Braintree, Stripe. Almost no one ever requires any additional paperwork, even when transferring from abroad, which is quite convenient.
But it will not always be so easy while you are in the country simply on a visa, and not as a permanent resident (you do not have a green card).