‘legitimate government’ isn’t really a thing. Many recognized countries are ruled by hereditary governments, or by autocrats who gained power in a coup. The legitimacy of such governments, andthe nationhood of the states, is recognized by other countries based on the foreign policy (mostly self interest) of those other countries. So, if you want to guess who would recognize a Gaza nation with Hamas as the ruling clique, ask yourself what governments would benifit from doing that.