Ah, but see, the OP doesn't reside in the US, at all. She may have a US SSN, but doesn't live here.

My personal experience and that of friends is that a SSN isn't necessarily required to open a U.S. bank account. For example, I have friends who are here in the US illegally. They have been here for years, and work here, but don't have legal residence. They have TIN's which they use to file taxes. Those are not a SSN, but they are sufficient to get a bank account - my friends have several. However, a TIN does not allow them to get credit cards and they don't have any of those.

However, I have yet to hear of a U.S. bank, online or otherwise, that will let an account be opened by someone without a U.S. address - even if that person has a SSN. So I would suggest that the OP find a friend or relative in the US whose address could be used to open the account.

Once the account's open, it may be less of an issue to change the address to an overseas one, assuming the friend/relative doesn't want to go through the task of continually forwarding mail.

This site, which I found by googling "expat banking", seems to confirm this thinking.