My wife lives in Canada, and just got her US residency, so I can tell you it's not easy.
She was able to get an Amex card but only after having a USA bank account. To get that account, I opened the account, then she went in with me and showed her Canadian passport, and they changed it to a joint account. Her Amex card was also based on a favorable credit history in Canada with Amex.
Even now, we are trying to get her a Hyatt card, and it's not easy. She has a green card and an SSN but her credit file in the USA hasn't hit, and even when it does, there won't be much there.
The banks are getting more and more strict about this stuff. I'm very sympathetic to your situation, but I think you'll have quite a hard time.