It isn't that the West didn't know about the Holocaust; it is that it chose to ignore it.
Here is an article in the Palestine Post from November 26, 1942 that was quite detailed as to what was happening to Jews in Poland, before the bulk of Jews were murdered:
In December 1942, many more details were published and widely disseminated. The genocide of the Jews was very well known by the end of 1942 in England, the United States and worldwide. (The following three articles were all from the Palestine Post, December 20, 1942):
London newspapers all published the information as well as ideas on how to help the remaining Jews:
Jewish agencies pleaded for help and prominent politicians were informed about the details of the Holocaust, many of whom professed their support:
And yet at this point there were still over 3 million more Jewish men, women and children who were fated to be butchered over the next two years, while the Allies did almost nothing to save them.