I used to work in museums. And there were generally two ways to break into the field. The first was to work an entry-level job and eventually move your way up. You would spend your first couple of years being an assistant to someone, answering phones, stuffing envelopes, and staffing fundraisers, with the idea being that you would already have your foot in the door when a better job came open. The second was to take on a position of high responsibilities in a tiny, understaffed (because underfunded) organization. That’s the route I took.
I worked on a staff of 4, which became a staff of 3, and then 2, and so I was in way over my head. And with nobody to mentor me because again: understaffed and underfunded.
Hopefully times are different now, because even then, in 2006, when I reached out to the larger well-established museum in town practically BEGGING someone to mentor me, I got no reply. At all.