I think you have some false assumptions, namely that "large numbers" of soldiers were involved in the holocaust, which is not true. Early in the war there were "einsatzgruppen" which had a few thousand, but these were disbanded or repurposed over time and most of the holocaust took place in great secrecy. All of the death camps, with the exception of Auschwitz-Birkenau, were located in remote locations and run by very small squads of men under the the direct control of Adolph Eichmann, who reported to Himmler. The execution areas in Auschwitz, which were located in the Birkenau area of the camp, were carefully segregated from the main parts of the camp and every effort was made to make Auschwitz look like nothing other than a work camp.
Before the war started there were no death camps, and all of the camps were publicized as work camps. Letters were allowed in out and the conditions were made relatively public.
After the war started, news concerning the camps was gradually decreased until the public received no information whatsoever, and most Germans and foreigners simply assumed the camps were no different than they were before the war. The death camps like Chelmo, Treblinka and Majdanek, were constructed in militarily controlled areas in complete secrecy. Noone even knew they existed except those immediately involved in their operations. Locals were removed for miles around the death camps, which were placed in remote areas to begin with.
The full dimensions of the holocaust did not become clear until the war was over and research gradually revealed the nature and extent of it. Even during the trials at Nuremberg, the prosecutors did not fully know of the existence of the death camps or understand how they were used, except Auschwitz. For example, a large number of prisoners escaped from Sobibor and could theoretically have testified to its existence, but nevertheless no major trial took place until 1965 and only 6 Germans were convicted. The total number of Germans involved at Sobibor was perhaps a few dozen at most.
In the immediate aftermath of the war, the Holocaust was represented by the emaciated corpses discovered at Dachau of which newsreels were taken, however, Dachau was not even a death camp. The prisoners died from starvation and cholera near the end of the war after food and water supplies were cut off.
In the years after the war 1945-1949, the German public was "re-educated" to become aware of the Holocaust, but the focus of "education" was on well-known aspects such as the camps in the western sectors such as Dachau, Buchenwald and on the use of slave labor in the factories, and on what was known of Auschwitz, which was limited because it had been destroyed and was in the Soviet sector. For this reason the full scope of the exterminations only gradually became clear, both to the Germans and the world at large, over the course of the 1950s and 1960s. In 1954, Gregory Frumkin writing in Switzerland, published a statistical book in which he tallied 6 million Jews as having disappeared from eastern Europe based on census data, and this was widely misinterpreted as a death count and publicized in that way. From the date though (1954) you can see that scope of the Holocaust was something that was revealed not all at once, but over time.