Today the Internet is the way to do business. This applies especially to the US, as they have invented the Internet.
It is possible to open a bank account, credit card, loan, or other financial services online. Identification by the customer is mainly provided by presenting a SSN along with a state ID number, which is most usually a state driver's license.
Being a NRA (Non Resident Alien) means that you usually do not have either one. Therefore opening a bank account online will not work. You need to find a local branch of your desired bank an apply there in person.
Sorry for this very inconvenient fact. :-)