Well, I am not an expert in the 'theory' of science, and there is considerable dispute over what we actually mean by the scientific method in terms of its everyday practice in the lab, but let me try to take my best shot at this.
At the time Copernicus announced his heliocentric model, there was not a scrap of evidence that even hinted that the Earth revolved around the Sun. In fact, from the practical standpoint, predictions made from Ptolemy's geocentric model and Copernicus's heliocentric model yielded much the same predictions for where the planets would be located in the sky as seen from Earth, for at least several decades after Copernicus went public with his model. His model, by the way, was purely geometric with NO dynamics in it. There was no discussion of the true space velocities of the planets, or the nature of the forces operating to make them move. His choice of putting the Sun at the center was purely one of taste and philosophy, not of some requirement by any observation.
Even by the time of Tycho Brahe, there was no way to 'falsify' Copernicus anymore than one could falsify the geocentric model. What changed was that Kepler deduced from the motion of Mars, that its orbit was not a circle but an ellipse. He also deduced two other 'laws' of planetary motion from the data accumulated by Tycho Brahe. The data and Kelper's Three Laws ,could not be accommodated by the Ptolmaic model, and even Copernicus' original model held that the planets orbited along circular paths. So one of the predictions by Copernicus, that planets moved on circular orbits, was 'falsified' .But what remained was that with only a minor modification, Copernicus' heliocentric model survived, but this time with the planets orbiting the Sun on elliptical paths. This could not be accommodated by a modification of the Ptolmaic model because this model required circular epicycles and deferents. So, the Ptolmaic model, and everything associated with it, had to be chucked in favor of Copernicus. Both the Ptolmaic and Copernican models could be falsified by the measurement of the true orbits of the planets, and only the Copernican model survived.
As for the issue of how you 'prove' that the Sun is really the center, this is done by measuring the mass of the Sun, and the motions of the stars, and showing that the Sun and stars cannot be rotating around the Earth given what we now know about the laws of physics. e