What led to the formation of the Palestine Liberation Organization (PLO)?The Rise and Interaction of Superpowers 1945-1962
The Palestine Liberation Organization was formed in 1964. It is recognized as the only legitimate representative of the Palestinian People. The United States considered the PLO a terrorist organization up until 1991. In 1993, the PLO realized that Israel had the right to live in peace and they rejected violence and terrorism.
The Arab League began the creation of an organization that represented the Palestinian people in 1964.
Its Statement of Proclamation of the Organization declared "... the right of the Palestinian Arab people to its sacred homeland Palestine and affirming the inevitability of the battle to liberate the usurped part from it, and its determination to bring out its effective revolutionary entity and the mobilization of the capabilities and potentialities and its material, military and spiritual forces".
Although you label this as having to do with the time period 1945 to 1962, the Palestine Liberation Organization did not come into existence until 1964. There is no one event that caused it to be created at that time.
What led to the formation of the PLO was the creation of the State of Israel. This happened in 1948. When this happened, many of the Palestinians who had been living in what was now Israel fled or were pushed out by the Israelis. They went to live in refugee camps in places like Lebanon and Jordan. The PLO was eventually created to represent these refugees.