I have never been asked to prove I am Jewish, but I often wondered how I could do it. My mother was born in Cairo and her mother in Damascus, and good luck in retrieving archives from hostile regimes (assuming they haven't been destroyed already). However, I brought two documents with me from Egypt: (1) A 1967 certificate saying I haven't been married before, signed by the Chief Rabbi of Egypt, and (2) My birth certificate, released by Egyptian authorities, which states also that I am Jewish. Would either or both be proof enough?
(Were Holocaust survivors emigrating to Israel asked to prove in writing they were Jewish?)