Copernicus himself cited some Ancient Greek and Roman sources in his work, which he saw as giving it some credibility (in his book, he traces all of his work back to the Ancients, esp. the Sun-worshiping Pythagoreans, because that aligns very much with his Renaissance values put on the recovery of Ancient knowledge). He would not have considered himself the first person to have the idea of heliocentrism. There are many pre-sentiments of heliocentrism, and many geo-heliocentric models that started to move in that direction (e.g., models like the one Tycho Brahe would later champion).

But he was the first person to try to work it out systematically: the try and reconcile how the idea of heliocentrism would work in a mathematical fashion, and to reconcile specific theory of planetary motion with the data. I think it is fair to make the argument that Copernicus was the first theory of heliocentrism that attempted to have a really scientific basis to it, and was not being put forward as a form of philosophy. (For this purpose, I'm using "scientific" simply to mean, "a theory of natural philosophy that is mathematical in nature and is meant to be in accord with observational data" — there are plenty of other definitions, and it can be a fuzzy category, but this is close to what most people imagine it to mean.)

Even Copernicus, of course, did not quite pull it off. His model had some significant errors in it, and was not compelling to most scientists and philosophers of his time. However his methods were interesting and useful, and the idea that motivated them did take off with other scientists who would credit Copernicus' effort as the first real step forward, even if it was incomplete. There are some historians who think Kepler ought to be given far more credit than he usually is for advancing heliocentrism; it was Kepler who really turned it into a viable system that worked well, by repairing some of the calculations (using ellipses instead of circles, for example), formulating specific laws of planetary motion, and demonstrating that they worked with the data very well (of course, the data had to be collected before that could be done). (Galileo gets a lot of attention here, and he should, but Kepler was probably more impactful on the scientific community.) It is for kicking off the "Copernican revolution" — the sequence of ideas and experiments and theories that would, hundreds of years after Copernicus' death, lead to the widespread acceptance of heliocentrism — that we typically credit Copernicus for. Crediting him for heliocentrism is just a short-hand form of that.