Is it standard to "pitch" gallery/museum exhibition ideas?

I suppose the better question is, how does one get an exhibit in a museum?
I’ve a great concept, and have done the research; and I’m in the process of planning to shoot photos with a cousin. Could I get in touch with a museum and ask if they’d have interest, or am I aiming way too high here? What are the barriers to entry I’m not aware of? I’m talking about producing something here…

(located in NYC)