My student visa is about to expire, and I’ve been accepted for a job here. Can I stay and work legally while I apply for a work visa?

Yes, if you file a timely change of status

You must apply for an H1B or other work visa and get approval before your F1 status or grace period ends.

If you're eligible for OPT/STEM OPT, you can work legally after graduation while your employer files for a work visa.