So, when does the parody begin?

Presently, it appears to be documentary with faux-Hitler narrating.

“Der Untergang” (2004) is a German film depicting events in Hitler’s Chancery leading up to his suicide as Soviet forces approach Berlin. The scene in which Hitler, played by Bruno Ganz, learns that Armeeabteilung Steiner (a German Army formation that existed largely on paper) was not going to stop the Russians, he raves and recriminates with his top military advisors.

That scene is frequently humorously overdubbed as a satirical commentary on some current disaster produced by similar delusional or incompetent leadership.

Click on “Der Untergang” (2004) for many more examples.