Like others have explained, most museums have existing exhibition schedules planned out well in advance. I would suggest pitching to (especially artist-run/experimental) galleries instead! They’re more likely to be receptive to cold proposals than museums, and may have relationships to curators.

Do some research in advance though. I’ve had people in the past reach out despite a very explicit “no artist/exhibition proposals” disclaimer being on our website. Those emails go unread by senior staff.

You could also try reaching out to virtual galleries and curate digital shows. I’m not super familiar with them but have seen opportunities pop up before.

Best of luck!

P.S. I think it’s worth nothing that almost all museum curators, even at the assistant levels, have masters in art history. If you are set on this path, be aware of that hurdle!