AF447 was in serious upset at 0210.
Not necessarily.
From a pure timing perspective, it would be sufficient to change the flight path 3,5° up. That would mean according to my rough calculation that about one minute later they would be at 38000 ft and 220kts if Throttles remained unchanged (admittedly that is not 100% correct as with the speed decrease the drag would reduce quite a bit so the engines would have some SET, so energy conservation is not 100% constant which it was at 270kts with level attitude for the given N1/EPR). OK, let's take 5° up. (Alternatively, cut the throttle back)
Then they would hit the stall.
As I mentioned the drop would not be immediately like a brick, but after some decelleration the plane might be dropping at vertical velocities towards terminal velocity. lets add another 30 secs for this transition phase. Add 30 secs for the initiation of the pull up.
And then 2 minutes down.
And here we go: 4 minutes.
Just pure speculation though, but at least it could fit.
But even if this was the case, the most important question would be:
WHY ?? And that's why we need the black boxes.
Edit:
What also remains a mystery to me in this scenario, even if it was possible from a timing point of view is the question if a Conventional Tail Airliner can really deep stall straight down. So far I always thought this was a 'privilege' of T- Tails.
The only way I thought this would be possible with Conventional Tail was with elevator or at least Trim full up.
If this assumption would be correct the question would be again: Why ?
/Edit