If structural integrity is in doubt ...

[PEI_3721]

The question should be what determines the speed/type of ‘rapid’ descent;- 'what is the nature of the problem?'.

A slowly climbing cabin could have been detected before a warning is given. Even at 10,000ft here is time for some remedial actions – check switches / close outflow valves – control the situation.

For a rapid (surprising) decompression – with the cabin altitude climbing rapidly, then a descent should be commenced immediately. There may be other system indications of what is happening which will subsequently indicate the necessary rate of descent.
Remember that you are more likely to kill passengers from hasty or misjudged actions than missing the required descent altitude by a few seconds. Beware of the actual safety altitude, no need to rush into mountains with a high rate descent.
The important issue is to get the oxygen masks on so that you can asses the situation and then decide on modifying the initial action ( SSR ) – remain in control and control the outcome.

It’s most unlikely that a rapid decompression will give ‘instantaneous’ flight / cabin altitude. Even with a window out the cabin should still have a supply of engine air and the outflow valves should be closed (and there’s always the Nun with a guitar who blocks the window).

I recall the story of a ‘Far East’ BAC 1-11 many years ago which suffered an ‘explosive’ decompression due to a ‘device’. This removed part of a fuselage panel; the crew completed a rapid, high speed emergency decent during which the power controls failed and thus required manual recovery. The FDR indicated that they pulled >3g, and with a hole in the side of the aircraft (BAC1-11 were built strong).
Some months later the same Captain suffered exactly the same symptoms; his response was to take things a little slower. With the advantage of experience, he managed the surprise - starly factor, assessed the situation (similarities), and chose a safe course of action.

In the absence of experience we have to think about these things before the event ( IC #4 ).
We should not be overly biased by a procedural training drill in simulator, few of these use realistic scenarios and might overlook the important assessment and adjustment phases.