Yes, it is possible to have a documentary of the Holocaust that lasts only thirty minutes.
Nuit et brouillard, or Night and Fog, was made in 1955, using both archival footage of the camps, as well as contemporary scenes.
The film is dramatic in a 1950s sense, with a heavy score and abrupt cuts. For modern viewers, more accustomed to certain images of the Holocaust, it may appear a bit thin.
Also, there is little specific mention of the special role the Jews played in the Holocaust. Certainly, many others were killed, but this film never takes mention of the overwhelming numbers of Jews killed during the Nazi era. The film is not about the Jews cost of the Holocaust.
Night and Fog has some value today as a way to view how the Holocaust was framed ten years after it occurred. Already, people were struggling with the enormity of it, and keeping the memory alive.