Yes this is possible and very easy.
WellsFargo is the bank to go to at the west coast, (deposit $1500 and you do not pay account fees)
TD at the east coast (deposit $500 and you do not pay account fees).
With both banks you get issued a
debit card. Your account opening deposit ($150), which you can spend immediately with your debit card.
BoA also accepts walk in customers.
You need a passport + drivers license, and a credit card to fund you deposit (WF) or
cash (TD). For both you do not need a US address (you do for BofA). A US cellphone number is easy (for account autentication, you can easily change this to a EU number once you are back in Europe.