Trying to assess what might have been done to prevent the Holocaust and why it was not done requires facing hard facts.
From January 1933 to August 1939, Nazi Germany engaged in an appalling persecution of the Jews under their control. The Jews lost their German citizenship and civil rights; they were excluded from the economy and society, and robbed of their possessions; and every effort was made to foster hostility toward Jews. The aim was to drive German Jews to emigrate. In 1938, Germany added Austria to the Reich. All this was widely reported in foreign countries.
Nevertheless, there were two great barriers to the flight of the Jews. On the one hand, there was a real reluctance on the part of many Jews to be driven out of their country by a bunch of louts who seemed unlikely to remain long in power. On the other hand, most countries were unwilling to take in many “ordinary” German refugees. First, Poland, Hungary, and Rumania were ferociously anti-Semitic societies. They didn’t want more Jews (or anyone else) added to their population; no Jew would think that pre-1939 Nazi Germany was a worse place than these countries. Then there was the Soviet Union. It not only oppressed and persecuted its inhabitants, but also was in the process of murdering hundreds of thousands of them.
That left countries to the West of Germany as a possible refuge. This meant France, Belgium, the Netherlands, Britain and its Commonwealth, and the United States. All were struggling with the economic catastrophe of the Depression. This meant that they were fighting against high unemployment without immense success. Taking in tens of thousands of refugees, let alone hundreds of thousands, would make the unemployment problems worse over the short-term. It would have financial costs that would have to be born by a country’s taxpayers for the benefit of non-citizens. Then, anti-Semitism existed as a real force in all of these countries, no matter how much politicians denied it or the press decried it. It wasn’t Nazi anti-Semitism. It was more “would you let your sister marry one?” and “there are too many in the universities” anti-Semitism. No less real and powerful for that. These factors made the refugee question politically explosive. The easiest course was to say “It is unfortunate and disgusting that the Jews under Nazi rule are being persecuted; it is to be hoped that “normal” Germans will reassert themselves; but in the meantime, there are limits to how many refugees we can take.”
A second phase began with the outbreak of the Second World War in September 1939. From this point onward, the Nazis tried to prevent Jews from leaving the lands that they controlled. Furthermore, the number of Jews under Nazi control expanded massively and rapidly. From August 1939 to August 1940, the number rose from about 800,000 to 3.2 million. By late Fall 1941, there probably were an additional 2.2 million. There were an additional 1.3 million under the control of German-allied states (Bulgaria, Rumania, Hungary, Italy). What Germany meant to do with its captives wasn’t known at first.
Along the way, the Germans defeated Poland, Denmark, Norway, the Low Countries, France, Yugoslavia, and Greece, and rocked the Soviet Union to its foundations. German victories brought into the war both Italy (1940) and Japan (1941). That is, German aggression overthrew the established system of powers and created an unprecedented global crisis.
 It was easier for the “prominenten”: scientists, writers and artists, political leaders.
 Just because the editors of the New York Times believed the erroneous reports from their Moscow correspondent doesn’t mean that people in Europe believed them.
 See, most recently, Richard Overy, Blood and Ruins: The Great Imperial War, 1931-1945 (2021).