My youngest briefly considered Museum Studies for undergrad, at least as a minor, though she was concerned about career prospects and earnings. She just finished up her freshman year, and the on campus job she found was at the university archives. It paid - not real well - but better than her sister’s undergrad job at the same university as a math TA.
She did have experience in archiving in high school, though something like that might be a place to start - somewhat museum related and would probably be a paying job.