Newton's Laws - Pushing on a heavy object

I'm trying to understand if a really heavy object on earth, say a mountain, would move if I push it with my bare hands. This sounds absurd but according to Newton's Laws, if I push against the mountain it will exert an equal and opposite force. I understand there are other forces like gravity and friction involved but does it mean that me pushing on it will effectively move the mountain and because of the astronomical difference in the mass between me and the mountain, the effect will be infinitesimally small? or is it that there will be absolutely zero displacement?

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