When did the world become aware of the Nazis' genocide of the Jews?
This depends upon what you mean by “genocide” and what you mean by “aware.”
The world, or at least the United States , was aware that the Nazi regime was oppressing the Jews, sometimes quite brutally, even before WWII broke out. There were American reporters in Germany up even after the war began. They knew some things about Jews being put (along with many other kinds of people) in concentration camps.
After the war broke out, people learned some things about what was going on. They knew, for instance, that Jews were suffering terribly. They knew about the creation of ghettos. However, they did not know about the mass killings that were taking place. There were stories of such things coming out of German-occupied Europe, but it was very hard to know whether such stories (which surely seemed incredible) were to be believed. They were not necessarily from sources that could absolutely be seen as credible.
The world first became officially aware of the Final Solution in late 1942. At that point, irrefutable proof was brought out of Europe and was confirmed by the government. So, the world knew parts of what was going on before WWII started. It learned a great deal more in 1942. It is probably fair to say that the full extent of the genocide was not known until after the war.