Can a few random interaction with cockpit controls result in a crash? Lets say a monkey / snake interacts with 3 random controls inside the cockpit within less than 3 seconds until the PIC / SIC can take control of the aircraft again. Could such interactions result in a configuration leading to a crash that could not be reversed in time?

Assume the following:


small commercial aircraft (e.g. A319, CRJ900)
short distance flight (e.g. LEJ -> FRA)
appropriate cruising altitude for this distance


Edit: (for clarification)


It was mentioned I mixed the technical terms controls and instruments. I mean anything that does something when its pressed. So any buttons, switches, flight controls, etc.
This question is aiming at quick interactions with controls, no prolonged input.
Assume the pilots make no errors after the incident.




Background:
I was recently telling a post-9/11 flyer that I was generally allowed to visit the cockpit during the flight (as a child, pre-2000s). That person was surprised that this was allowed and asked what would've happened if a kid managed to interact with the cockpit.
Neglecting the fact that the pilots would probably intervene before any controls were touched it got me thinking if it would even be possible to doom a plane with a few quick interactions.
There's a real-life example that seems very similar: Aeroflot 593. The pilots let two children sit in the cockpit while the aircraft was on autopilot. One of the children pushed the control column for 30 seconds, which disengaged the autopilot and started a steep turn. The pilots tried to recover but the aircraft stalled and crashed, killing everyone on board.