There was no limits to immigration to palestine until the White Paper came out, HOWEVER it was not seen as desireable to go, there was starvation , hostile neighbors etc. It was seen as a lower standard of living Palestine in the 30’s than Europe was, The USA was alaways seen as better
However there was a fairly large German Jewish emigration in the 30’s with the advent of Nazism.
Better a physical death in Europe than a spiritual death in America.
This is nonsense, Did Rav Moshe , Rav Aharon Kotler or others who were able to escape hold by this shitta.
Those who said to stay were wrong, What they should have done is send Rabbaim to the USA and built Yeshivas. Already around the year 1900 New York City had the largest jewish population in the World and it might have been the richest as well as many Roshei Yeshivot went to NY to Fund Raise, but did not say to use the money there to built yeshivas in NY