The war started the day after the UN resolution, in November 20 1947. The war wasn’t caused by the expulsion of Arabs. The Arab states refusing to recognize the creation of a Jewish state caused the war: https://en.wikipedia.org/wiki/1948_Palestine_war
> The war had two main phases, the first being the 1947–1948 civil war, which began on 30 November 1947,[19] a day after the United Nations voted to adopt the Partition Plan for Palestine, which divided the territory into Jewish and Arab sovereign states, and an international Jerusalem (UN Resolution 181). Partition was accepted by the Jewish leadership, but rejected by Palestinian Arab leaders and the Arab states.
> The war had two main phases, the first being the 1947–1948 civil war, which began on 30 November 1947,[19] a day after the United Nations voted to adopt the Partition Plan for Palestine, which divided the territory into Jewish and Arab sovereign states, and an international Jerusalem (UN Resolution 181). Partition was accepted by the Jewish leadership, but rejected by Palestinian Arab leaders and the Arab states.