That too can be done although it is difficult. KYC "regulations" do not require a physical address in the US. Most US banks do want a US shipping address to send your statements, checkbook, debit card and such to, which is easy enough to take care of. Most also will say that they require the foreign resident physically come to the bank to open the account. The most common answer you'll get is that it's not possible, but that is not true at all.

EverBank at least used to open accounts for foreign residents by mail, although they did want a lot of documents.

Most of the biggest banks will open accounts for foreign residents too. Just visit their site and look around. The process may be not worth the trouble or cost, but it's very possible to do, especially if your initial deposit will be substantial and they understand the reasons that you want to open an account there.

You do not need a Social Security Number to bank in the USA but having an SSN will almost guarantee that opening a bank account is an easy task. It's often treated as a well known fact that you must have a valid SSN or the bank cannot legally open an account for you, but in actual fact that it not true.