Most American Banks demand ways of confirming your name, date of birth, address, and ID number in order to open an account. However, customers with no SSN number are eligible to use their ITIN number in the bank fillings.
Meanwhile, some banks such as Citibank and PNC would accept a passport number and country of issuance, an alien identification card number, or another government-issued ID number to open an account if you don’t have an SSN or ITIN number.