Unfortunately nowadays opening a bank account in the US is a real challenge. Although I heard some rumors about banks that open accounts for international clients without physical presence those rumors typically stay rumors, or those solutions are very short lived.
As a non-US person you can register a company in the US and obtain an EIN, but you would need to travel to the US to open a bank account. Keep in mind that the minimum you would be asked to present is company documents (Articles, EIN Letter), your personal photo ID, and a proof of address (typically a bank statement from your bank in your country, translated to English and notarized if its in a different language).
Some banks would require you to show direct connection to the company (through Operating Agreement, a letter form an attorney or other document, if the Articles do not list your name). I would recommend you to visit several bigger banks when you come to the US and see which one will give you less trouble opening an account. We can help you open an account in JP Morgan Chase if you can travel to New York City.