@Soonermom, I’ll ditto what @ohmmom said - my freshman D does not have a car in Norman either, and has not found it to be a problem at all. We even offered recently to let her take the car she has shared with siblings, for next semester, and she said she’d rather wait until next year when she is in an apartment. Surprised me, for sure!
Regarding moving a college student across-country, our older D attends a school far from us. We used the Bed Bath and Beyond service that allows you to purchase items at your local store which you then pick up at a store close to the university. We did that for everything from bedding and towels to hangers, bathroom caddy, etc. Then, she and I flew there for move-in, so with checked luggage for two people (I traveled lightly with one carryon, checking 2 of her bags as mine), and a shipped box or two later on (winter clothes etc.), she was good to go.