My dad just posed this question to me, and I thought what better place to ask than Reddit. How early in the war did the allies know about the Nazi's extermination camps? Thanks.
The answer is unfortunately, very very early. Chelmno, and the Operation Reinhard extermination camps were built in late 1941-early 1942. Many Jewish papers were actually reporting on the Holocaust as it happened, though with varying levels of accuracy and depth of information based on the information that they were able to get out of Europe. The mainstream American press was reporting parallel to this, but often engaged in hiding these articles deep in the paper. In late 1942 The New Republic reported on both gas vans and extermination camps using stationary gas chambers. The Jewish wire service the JTA was reporting on Chelmno by spring of 1942 when the camp had been operational for less than six months. They were reporting on estimated numbers of dead, who was being killed (mostly Jews from Lodz and the surrounding areas), and how they were being killed (through carbon monoxide poisoning in gas vans). The largest Yiddish newspaper, the Forverts, reported these findings as soon as the information was available. The New York Times on the other hand had unsubscribed to the JTA, had no foreign correspondent in Poland, and often failed to report, or failed to report in a timely manner/in a section of the paper people actually read, often hiding articles among advertisements.
Many of the mass shootings carried out by the Einsatzgruppen were widely reported, especially on the Soviet side, as they happened, though with varying levels of accuracy (the victims were often reported as Soviet citizens rather than Jews). And given that the Einsatzgruppen followed the Wehrmacht closely, the Soviets had no illusions about what the Nazis were doing. Many of the mass graves in contested areas were uncovered and photographed by the mostly Jewish Soviet photojournalism groups. People like Ilya Ehrenberg and Vasily Grossman both reported on the Holocaust in the Soviet Union as it happened.
Through the efforts of people like Szmul Zygielbojm and others such as Jan Karski, mostly members of Jewish undergrounds and partisan units, the Western Allies as well as the Soviets knew about the mass shootings and the death camps in detail soon after they began. As a Jewish member of the Polish Government in Exile in London, Zygielbojm was in contact with the Jewish underground and was reporting on the Holocaust with great accuracy by early 1942, and some information on the Einsatzgruppen was known even before that. Despite this, Churchill's government did not lift the White Paper on emigration to Mandate Palestine and the US did not change their quota policies even after the war. The reason the number "6 million" was able to be reported so quickly after the war, is that there were Jews attempting to keep at least a vague count of the likely number of dead as it was happening. These events were reported in both mainstream and Jewish papers in all the Western Allied countries, and the events were known extensively by these governments, and yet both Britain and the US maintained caps on Jewish refugees trying to flee Europe, either to free Western countries or to Mandate Palestine, even after they knew about the mass killings.
https://newrepublic.com/article/118800/first-american-report-holocaust
Buried by the Times