I'm not sure what you mean by "cover up", there were different stages of the Holocaust, and most of the covering up you've seen probably refers to a point were they were on the retreat and knew that the camps were likely to fall into the hands of the allies. But the Nazi government never hid to it's people that it was on a mission to exterminate the what it say as inferior races via Vernichtungskrieg(War of Extermination)

Most of the death camps were not in places where the German citizen would stumble onto, many weren't even in Germany, but their existence was not state secrets and many Germans would have interacted with them by either working in the camps or in the transport of logistics.

I guess it would have been pretty obvious for anybody that a genocide had been commited.

Hitler has been quoted saying, and I'm paraphrasing here "Who talks about the Native Americans, or the Armenians". He compared his conquest of Europe to Americas conquest of its West. Perhaps he foresaw himself partaking in similar apologetics

Did they planned to reveal what had been done after the facts or make up stories to explain the disappearance of jews without appearing guilty?

Guilty to whom? The Americans who had completed their own gencoide? The Europeans who were under their control? The Japanese who were doing the same thing in the East? The Germans who were taught that Jews and Slaves were evil inferior races that must be destroyed?

The Nazi's didn't plan to lose, and if they had won there wouldn't have been much explaining to do. It should be noted that according to their plans, they would have killed way more Russians and slavic people than Jews by the end of the conquest. The next generations would have likely been taught that the victory in the war was a great thing, and the death of women and children was an unfortunate result of the conditions that result in war.

You'll note that according to LeMay America killed around 20% of North Korea's civilian population during the Korean War via bombing, did the US government feel the need to explain that the American people? Do most Americans even know or care that it happened? And consider that America is much more open society than the Third Reich.

I have previously collected answers by /u/hannahstohelit and /u/commiespaceinvader and /u/estherke in response to Did the Nazi State ever draw an strategy on how to “communicate”, in case of victory in the War, what had happened with the Jews?

In 1939, the Nazi government started T4 euthanasia program for the "incurably sick", mentally challenged etc. This is a couple of years before the large-scale extermination program for the Jews, gypsies and others began. T4 killed about 70k people and was a pilot program to test out a lot of the techniques that were later used.

The T4 program was run with a bit more openness and largely in the public view. It began attracting a lot of opposition, especially from the church. Generally the feeling was that the German people disapproved of the program that was killing their own family members. So Hitler canceled the program after about a year.

The lesson learned by the govt was that the German people support such extermination programs but don't want to know about them. This was in line with the larger Nazi ideology that viewed killing (even of Jews) as sinful but believed that a good Nazi needs to commit such a sin on behalf of his society in order to rid the world of Jews. So no need to make the whole German society complicit in the murders. Accordingly, the latter extermination programs were a bit more hush hush and wink wink. Nobody needed to know although everybody kinda knew.

For T4 program see Richard Evans: Third Reich in Power

For Nazi thinking around killing see: Timothy Snyder Bloodlands (last chapter)

Robert Harris wrote an alternate history called Fatherland that deals with exactly your question: the Nazis won the war and twenty years have passed. How do common German people think about the missing Jews. His speculation is that while everyone knows that something was done to the Jews nobody knows exactly what. Certainly no one knows or wants to know the full extent of the horror of the Holocaust. That sounds about right.