Unfortunately, the answer would be NO!
If you have standard life in USA, you must have a bank account to have electric billed, water billed, CREDIT CARDS, to rent a house or Apartment you must have “BANK information” showing credit risks. Cellphone, have to have credit card for account or use a Pre-Paid limited access phone.
If you apply for a job, how will you cash the checks? Most PayCheck cashing places charge a % of check as commission.
So if you live where you can barter, or use cash at ALL TIMES, and only have a check once in a while, sure no bank account.
Live in a city, get a bank account