I think people are making this too complicated.
To me it’s no different than when I move to PA from CA for school.
Your kid has a set of primary ID: Passport and a Social Security Card. If you you need a social security card, then just go to a local SS Office with passport / birth certificate and apply for one.
Go to a local bank and open an account with passport / SS Card.
Most places will rent / lease to a student with just these ID. Sometimes parents will need cosigning. But cash talks.
If your kid knows how to drive, then go to a local DMV office and apply for a drivers license. DMV does a document search to make sure there is not already an existing DL in another state. If there is, you will need to surrender it to get the new one.
You are basically looking for a place to live and set up life and not setting up “residency” for voting or tax purposes. No business will turn down good money from people with proper ID. But a Passport and SS card is a must to get things started.