I have experience in pressurizing and depressurizing transport aircraft on the ground (done for the purpose of locating structural defects). We would pressurize to about 20% over normal in-flight differential pressure using two large road works compressors.
For safety we devised several means of depressurizing rapidly. Our main method used a purpose built valve installed into a modified over-wing exit door, while our backup was through the toilet cleaning valves. Typical times for reducing from maximum in-flight differential pressure to sea level were on the order of 30 seconds for a 707 size aircraft.
During the development process the owner once had several technicians inside the aircraft. They reported that the depressurization process was a “wild ride”, in which they could not see or hear anything. It was so disorienting that they were unable to concentrate on their duties. And this was done at about 20C, not at -40C.
If D-AIPX experienced such a rapid depressurization at FL380, I can easily understand why the pilots might not have been able to put on their O2 masks before they lost consciousness!