Would Israel exist if the United States had let in a million mostly Jewish refugees in the 1930’s and 1940’s?

Almost certainly not. Israel came to be because of the intense need for a place of safety for the Jews of Europe. There was nowhere to go so we created one. If Franklin Roosevelt had been less of an anti-Semite than his contemporaries and used his pen to admit a million refugees then the need for Israel would have been much lower. The anti-Semites in the Middle East the US Department of State and Whitehall would have probably been able to stop Israel’s emergence as a nation.