Cold engine being flooded by a mashed pedal I can't imagine why it would protest idling smooth. Though either way sounds like a sensor is probably on its way out. But normal cold engine idle will be a rev that peaks close to 2000rpm right after you start the car and in my case almost always dropped off by the time I had the car rolling out of the driveway a minute or less later. Might be longer if the car is sitting in very cold temps vs just cold enough to get some ice to form on the windows over night etc.
Dirty - or bad grounding cable could also contribute to this