Your guess is a catch - please see the attached 2 pictures. Thus, I have to tell you the whole story, so you'll get one more tip for your next guess. The filter seems very delicious for someone which I didn't catch (likely a mouse). But these pictures are 1 month old and the same day when I found the intrusion, I installed new filter and I cleaned the debris in the MAF, between its plastic grid and the metal mesh behind it, debris is shown on the second picture.
The effect which I initially described (the idle RPM oscillations when the car is cold and just after the engine is started) actually is more than an year old. But two months ago it get even worst - for ex. when the car waits on a street light, even the engine coolant
is at its nominal temperature, due to these deep RPM changes, without touching the gas pedal, sometimes it died and needed a restart. So, the self running up-down RPM started to happen not only in the morning, when it is cold, but also anytime later. Then, I found and replaced the eaten filter which led back to the old effect – only in the morning while it is still cold.
Now I am searching for where to buy and what kind a MAF sensor but meanwhile you may have additional ideas.