Organizing LLC is not a problem for non-residents at all — you can do it either yourself (could be tricky if you don't know what to do) or use some incorporation service (there are plenty of them available).

Getting a bank account for it is way more tricky. First of all, you'll need a EIN for your LLC, which you can get with your own SSN or ITIN only. Since you're not a resident, you're not eligible for SSN, and getting ITIN is a little bit of "catch-22" problem.

And even if you'll get ITIN and, respectively, EIN, you might have hard times opening a bank account. I personally was able to do that by e-mail/mail, but I was introduced to financial specialist by a friend of mine.