In the 1930s, not only Germany but many other countries in Europe (Hungary, Romania, Italy as examples) passed various antisemitic laws that limited Jewish participation in the civil service, professions, education (both as teachers and students especially at universities). This was a sharp and painful reversal of the gains made in the last 100 years. Antisemitism and antisemitic parties were on the rise elsewhere in Europe if the legal limitations were not there (think France for example). In Poland, after the war, there were pogroms against Jewish survivors and reclamation of property was resisted, often violently. All of this would add to the basic driver behind Zionism that Jews could only be truly free and secure in their own state, so emigration to Palestine is likely to see a huge bump.
The UK, and the USA, both of which saw no occupation (and therefore no direct effect of the Holocaust) both had significant antisemitism. Quotas for university and professional school attendance, restricted housing including entire subdivision and towns, and much more. Both the UK and the USA, especially the latter, had severe limits on Jewish immigration and the USA, even after the Holocaust, was stingy in accepting Jewish immigrants. If there is no Holocaust, or it is much reduced due to less German success in the war I can't see the USA opening immigration quotas even as much as it did postwar OTL and the efforts to keep Jews out of the western hemisphere that occurred OTL will probably continue. The Holocaust did much to make overt antisemitism less acceptable, although OTL quotas in Ivy League colleges and housing restrictions continued until the early 1960s.
The point of all of this is that in the scenario absent a Holocaust, or one that is much reduced there will be just as much of Zionist drive as OTL. All of the countries that refused to accept many or even any Jews prior to the war in this scenario are unlikely to change policies in any significant way, so where do the Jews who want to leave go to if not Israel. Obviously the borders will be different, timing will be different but since the plan for a Jewish state (and Arab state) is in place... FWIW NONE of the states created during decolonialization, including Syria, Jordan, Lebanon were brought in to being by UN fiat or vote and did not need it for legitimization. No other territories that were mandatory either from the League of Nations or the UN had a "vote" to establish them. The UN got involved because the UK punted the problem, not because it was necessary.