You need SSN to operate that a/c
With that and a passport you can easily walk into a bank and open a checking account.
I just went though trying to get an ITIN for my spouse so we could file a joint tax return. After waiting for 5 weeks, they rejected the application because we didn't attach a copy of a previous tax return--which we don't have, so it's a catch 22 if I ever saw one. I'm certain that requirement is bogus on their part, but it meant we had to file for an extension on the tax return until we could get it sorted out. If it's that much trouble when you are a legal resident, I can't imagine the process for a non-resident.