You may not need a Social Security number, but you will need some form of identification (typically a passport, Florida ID, consular card.) Call the local branch in advance if you have particular questions.
Review some options in your community
View a list of options throughout Miami-Dade County.
Open your new account
Someone at the bank or credit union will walk you through the entire process. They can even connect you to free money management training classes to help you get the most from your new account.