lol.. j/k. But I think it will be much easier if you setup a corporation offshore first. Really depends on what you plan to do with it. But for example, usually when you setup a corp in a place like Dominica, the company who does the filing and paperwork for you will also have some banks around the world that they will give you an introduction to as part of the service.
Search google for “offshore corporation” and you will find a lot of legal companies who will set you up with paper work and do the filing for you.
Depending on what you will use it for, (tax shelter, passthrough, whatever) its hard to say whats best. But I can tell you that some places even having a tax treaty with the USA, also have a 0% tax rate for corporations in their country owned by foreigners.. so it is a much much better alternative to using your US company or personal name to setup the offshore accounts.
For example, you can setup a corporation in Dominica with a 0% corporate tax rate, then with an introduction from the company who setup your corporation, you can setup bank accounts in cypress and in st. vincent. (be sure to confirm with them before hand, which countries they offer an introduction to banks in)
If done proper, you can shelter yourself quite well from being taxed out the yin yang. And legally. Just remember any money you transfer to a personal account will be taxable. But of course, some of these banks offshore offer you a bank card that could literally withdraw $20k or $50k per day from bank machines.. without ever passing through a personal account..
Anyway Im not a lawyer or any kind of expert, and I dont personally do anything like what Im describing.. just food for thought..
But as far as having a low minimum balance requirement, cypress banks are pretty good.. and the account opening process does happen by mail and email once you have the introduction.