to open a bank account in United States, you MUST have a valid SS#
if you would like to apply for one, go to directdepositcard.com
when you provide your SS#, there is a software called city something and that software checks your SS# with the data you've provided to make sure if it matches what's on database. like your mailing address, your real name, your birth date etc. so there is no way around it. specialy after Patriot Act, things got tougher.
"The USA PATRIOT Act is a Federal Law that requires all financial institutions to obtain, verify and record information that identifies each person who opens an account. You will be asked to provide your name, address, date of birth, and other information that will allow us to identify you. You may also be asked to provide documentation as proof of identification."