Present a school ID of a WA state school.

No school ID because you are not in school? Then you've lost your privilege to drive. U.S. states, and several Canadian provinces are doing their utmost to keep kids from driving cars.

Anyway, I suspect WA DMV would take a bank account statement, a social security check, etc. as proof of residence for someone who did not have a job but was a new resident of WA. Of course the other way to get a DL would be to get a speeding ticket in WA and tell the state trooper your predicament.