Why did GOD let the Holocaust happen?
Your question assumes a God who actively interferes with human history; that is a very questionable premise. Most philosophies and most religions take as a starting point the creation of Man with certain traits, including free will, etc., and then view history as the acting out of Man’s free will. The Seven Deadly Sins are all the reason we need to understand how cruelty, genocide, and war itself comes into being. God does not interfere with historical events, and the Holocaust is just one of dozens of atrocities, from the Greek/Roman wars to Kosovo, to 9/11. The other way to approach a rationalization of this atrocity is to remember the truth: “We cannot know God’s will; we are not privy to God’s designs.” Perhaps the Holocaust made way for a Jewish Homeland, or perhaps the entire World War II was part of God’s design to prevent a World War III, or to create the United Nations or the European Union. The point, as Thomas Aquinas tried to explain, is that we do not approach our beliefs with logic, but with faith.