The 1949 war ends in tragedy for the Israelis for some reason (we can find one), and they end up sent to Florida (if there is anywhere that should be a Jewish homeland it's the gold coast), where they establish an Israel-in-exile, complete with an IDF (seconded to the Florida National Guard), with a decent amount of Legitimacy. Later on the Cubans and Israelis end up fighting over some reason (Who "Gets" Miami?), leading to War, and the IDF completely dominating the Cubans, ending with IDF tanks peacefully disembarking from a couple of (rented) Ferries in Guanabacoa Harbor (that's in Havanna).