The independence of Jewish people was negotiated over decades of peaceful diplomacy, and was voted for at the UN in 1947 by a big majority. The idea they did not achieve statehood by peaceful negotiation and legal means is false. That is exactly what they did.
Jews had been told they would get their independence and safety, for decades, by the British. The Peel commission had outlined plans for this and the Arabs rejected it. The Arabs were angry at the idea of a Jewish state, and launched themselves long campaigns of violence, terror attacks and ongoing riots which resulted in many deaths.
If you read the history of this time, the Brits were terrified of the Arabs - not the Jews - which is why they capitulated and banned Jewish immigration with the White Paper. And that White Paper, as you say, almost completely banned Jewish immigration to Israel from 1939, leading to the needless deaths of millions of Jews under the hands of Hitler.
The bulk spate of Jewish violence and strike action began immediately after that in 1939, and had no effect at all on the decision to move ahead. The white paper was enacted regardless and all those Jews were left to die.
It was only at the end of WWII when it was made clear 6 million Jews had just been murdered as the world did absolutely nothing, that Britain rescinded the White Paper and even then, they continued with the immigration ban. Holocaust survivors tried to get to Israel and the British stopped them, which led to violent resistance. Immigrants were detained by the British in camps on Cyprus. Stateless. Mostly children. Mostly OPHANS.
And that didn't end until May 1948 when the British mandate completely withdrew.
If you take a historical perspective of the events leading to the establishment of Israel as a modern state, it is one of the few in history which was established by diplomacy, negotiation and a legal means of international consensus. Most were established with swords and guns.
The reasons for it's success were many - it was agreed by the Peel commission years BEFORE the Holocaust that Jews had a legitimate claim to statehood, but factors such as Holocaust guilt, countries not wanting to take in Jews themselves, and serious antisemitism across the MENA region were the primary causational factors.