They absolutely tried to cover up evidence. One of the most prominent examples was in November 1944 when Himmler ordered the destruction of the gas champers and crematoriums in Auschwitz-Birkenau. Nazis burned documents, hid bodies, forced prisoners to march inward to the heart a Germany. Even in the latest days of the war the Nazis devoted massive amounts of resources to still furthering the Holocaust and after a certain point, to hide evidence of it.

Its true the Nazis were fanatical about the Holocaust. In the core of Nazi ideology was a racial superiority in some form of another over non-Aryans. Of course this was nothing more than political rather than racial. Jews were seen as the enemy, as a scapegoat, the Finns and Iranians seen as honorary Aryans because they could be useful to the war effort. The use of the Jews as a scapegoat was the main engine of the political machine. It drove everything the Germans did. They were fanatical about their documentation of it due to that. The Germans recorded NEARLY EVERYTHING about the process. They took pictures, tracked the movement, date of death, valuables, family, nearly everything they could about prisoners. The Nazis kept better track of their victims than the Allies did to Prisoners of War.

By mid-late 1944 the war was all but over, most high ranking Germans saw that, including many orchestrating the Holocaust. While propaganda worked to keep the lower ranks with high morale, or enough to fight, the upper ranks were more worried about how they'd be treated after the war. They weren't idiots. If you were robbing banks and suddenly you started getting chased by cops, by all means, you'd try to save yourself in some way too, theres no getting out of it now.

After the war, many, many Nazi criminals, all that were alive anyways, were put on trial. Even so, Heinrich Himmler, the main designer of the Holocaust, still killed himself in British captivity after the war. In the Nuremberg Trails, some of the most prominent members of the German government were put on trial, and most put to death. Notable people included Ernst Kaltenbrunner, the head of the internal intelligence of Germany, known as the Eyes of the police while the Gestapo were the hands. Albert Speer, architect of Hitler and saw the use of heavy amounts of slave labor, as evidenced with many, many letters between him and other high ranking officials such as Kaltenbrunner, and Fritz Sauckel, who was also put to death for his organization of slave labor.

Not only this, but subsequent trials such as the TWELVE subsequent US Nuremberg Military Trials (NMT). These included the Doctors' Trial, which saw the trial of 23 Nazi physicians who were involved in the euthanasia of undesirables. Said undesirables weren't necessarily Jews, but were mostly those with undesirable physical attributes, which contributed to the deaths of nearly 300,000 people. There was the Pohl trial, of many SS nazi officers including Pohl, a Lt. General in the Waffen SS; of which, most were imprisoned or hanged. Also the trial of the Einsatzgruppen. The Einstatzgruppen were mobile SS death squads, and because of this task, all but one of the defendants were imprisoned, hanged, or died in custody. Still, further trials such as the Dacau Trials, Auschwitz Trials, Belsen Trials, Belzec Trials, and the Ravensbruck Trials saw many involved people in concentration and labor camps put to court for their actions.

There was no doubt in anybody's mind that the Nazis, especially the high ranking ones, were going to pay for their actions. The Nazis knew this too, the war was over by 1945 without a doubt, their best bet was to save themselves for the following years. But it was close to impossible. The Nazis in the early war and prosecution of those in the Holocaust saw such confidence that they happily wrote down what happened, what they did, about the prisoners, their thoughts, messages to eachother, they didn't think they'd ever get caught.

There is an interesting theory of sorts after the war ended. Theres a common saying that once Germany surrendered, no more Nazis existed. And thats not just because the Nazi party ceased to exist, it was because for a brief period, the Nazi ideology also ceased to exist. Suddenly, nobody was a Nazi. They were following orders. They entered the SS to advance their career. They didn't really know what they were doing. They were forced to do it. Anything they could say to get away from the guilt of their crimes. In post war Germany it was called "Stunde Null", or Hour Zero. A 100% complete transformation of Germany who vehemently opposed any fascist or Nazi ideology. It was rather surprising however considering that 10% of Germany had joined the Nazi party.

Consider for a moment what it would be like near the end of the war. There is no point in trying to be proud of what you've done. Hitler was dead. Germany was more occupied than it was free, its allies turned against them, camps were being liberated. What else exactly would you do? Of course they were scared of being held guilty for what they've done, and those suspicions were right. In the late war, American soldiers would often times outright kill SS soldiers, Soviets wouldn't even give officers the chance to live, and to think they'd be kind after the war? Its easy to believe that all Nazis were brainwashed and 100% devoted the Holocaust but they were conscious of their actions and even more conscious of the consequences as the war drew to a close.

For further reading I'd suggest looking at Harvard's Documentation of the Nuremberg Trials to get an idea of the evidence used against the most important Nazi officials for their crimes.