Pumping the gas pedal doesn't really do anything. That's just an air flap (throttle plate) in a fuel injected car. You can dance on that pedal for ten hours and it won't put one drop of gas in your engine.
Having said that, the position of the throttle plate does send a signal to the computer. Ideally, on a cold day the gas pedal should barely be touched. A cold engine should be harder to start with the gas pedal in motion than if it is closed----so your actions suggest that the gas pedal has nothing to do with it and that maybe you have a sensor problem related to cold start enrichment.
Best thing to do is read the owner's manual on the proper way to start the car. All cars are a bit different here. Since you are under warranty, I'd take it back and have them "dial it in" and make sure you are getting proper fuel enrichment on cold start.