If someone was born in Lida or Haifa 1945 what passport would he get if the state of Israel did not exist yet?
In the interwar period the people in that region were under a British Mandate and would have carried passports designating them British subjects (but not UK citizens). Sort of like how it used to be for some in the Caribbean before independence. Prior to that they were Ottoman subjects.
If he got it in 1945, possibly a British passport, because the British ruled Israel at that time, but I think it would say Palestine. After 1948, if he was Jewish or had been living in the area that became Israel in 1948 when it became Israel, then an Israeli passport. After 1948, if he was not Jewish and had been living in the West Bank in 1948, then Jordanian. After 1948, if he was not Jewish and had been living in Gaza in 1948, then Egyptian.