The Apocalypse is a phenomenon slowly taking effect over the course of the events of Wolfenstein: Youngblood, and a good portion of time before that.
Upon reuniting with his two daughters, B.J. revealed that before dying to his hands, Hitler ordered the construction of a weather manipulating doomsday device. Knowing full well B.J. was going to come and take his life, Hitler programmed a fail-safe protocol in the device which would activate upon his demise, so he could take the world down with him.
After B.J. killed him, the device activated and it was too late to reverse the process. The device caused the weather patterns on Earth to behave erratically, with freak thunder storms, tsunamis and numerous natural disasters. Newspapers such as Die Neue Wahrheit produced in Germany often deny the nature of the apocalypse, claiming that "Aryans aren't afraid of a little weather" while Nazi meteorological organizations have attempted to calm a frightened European populace by declaring a new fifth season based off the apocalypse, called Sturmzeit. Some factions within the Reich, apparently aware of the nature of Hitler's doomsday device, have plotted to topple the Berlin regime in order to stop the impending apocalypse by evacuating the Reich to another dimension using Da'at Yichud technology. Based on Set Roth's calculation, in the next few decades, the Earth would not be able to sustain human life any longer. As the result, the God Key is utilized to create an inter-dimensional gateway to evacuate mankind to another world to survive.
The event is similar to Operation Cinder from the Star Wars franchise, a protocol Emperor Palpatine conceived for orbital bombardment on all planets along with the Galactic Empire as punishment for their failure of not preventing his death at the Battle of Endor, taking the galaxy along with him.