Heliocentrism did not start with Copernicus, and Copernicus's theory was not the one accepted, he still had circular orbits and equants. It is Kepler's version that became the consensus after Newton derived elliptic orbits from the inverse square law in Principia (1687). That "proved" it to most scientists. We can count from around 270 BC, when Aristarchus first suggested the idea, or from 1533, when Copernicus reintroduced it in a much more elaborate from, or from 1609 when Kepler replaced circles by ellipses. Wikipedia gives a very detailed account of history that would answer the question for any starting date, and under any interpretation of "prove".
Keep in mind however that under both Newtonian and relativistic physics the question of what revolves around what is subtle. A reference frame can be attached to both the Sun and the Earth, and either one will then revolve around the other in it. We need a way to select a preferred frame, for example according to the simplest description of dynamics. For the two of them that would be the frame attached to the center of their masses (which is inside the Sun because Earth is so much lighter, but not at its center), and they both revolve around it.