Could God have prevented the Holocaust? Yes, He could have. He could also have prevented Stalin’s massacres in the U.S.S.R., the Spanish Inquisition’s torture of dissidents, and Nero’s reign of terror. In each case, God allowed evil men to exercise a certain amount of power for a short period of time.
Ultimately, we do not know the reasons for what God allows. His ways and thoughts are infinitely higher than ours (Isaiah 55:8-9). His sovereign plan takes in the whole scope of history, past, present, and future, encompassing every possible course of action, every cause and effect, every potentiality, and every contingency. There is no way we could possibly fathom the intricacies of His design. By faith, we trust that His plan is the best plan possible for restoring fallen humanity and a cursed world to righteousness and blessing.
But we can understand this: God’s permission is not the same as His approval. God permitted Adam to eat of the forbidden tree, but He did not approve of the action. In the same way, God’s allowing the Holocaust in no way suggests His approval of it. God is grieved by the sinfulness of man and the hardness of his heart (Genesis 6:6; Mark 3:5).
We also know that God has done everything possible to redeem us from the sin which would destroy us. He gave His only Son, who sacrificed His life for our sin and took our penalty. All who turn to Jesus Christ in faith are saved. The sin in this world, and horrors such as the Holocaust, are a direct result of mankind’s continued rebellion against God.