Yes. People have been taught that the earth revolves around the sun, and sometimes we use it as a way to be smug about how much smarter we are than the ancients. But schools do a huge disservice to students by not showing them that there's not in fact any way to know this from the information the ancients had available to them. About all you can infer from the way the sun changes position in the sky is that some kind of movement is happening. Because the earth feels solid under your feet you might assume that only the sun, planets, and stars are moving. This is valid according to Occam's Razor.
Indeed for hundreds of years western astronomers predicted the locations of the planets using epicycles and not by calculating orbits assuming a heliocentric system. And it worked! Beautifully! The earth-centric model has excellent predictive power. It explained everything the ancients were aware of.
This is all as a lesson in both humility and in recognizing that our ancestors were not stupid or lacking reason. They just didn't have the tools we have. And for all that the heliocentric seems obvious, remember that it is only obvious because we have been taught it. Our ancestors had been taught an earth-centric model instead, and it was obvious to them.
To turn that on its head, it's a wonderful teaching moment to ask a room full of smart students to try and prove (or even convincingly argue) that the Earth moves around the sun. A great way to get people to examine their assumptions and look afresh at the world around them.
As you say, it is indeed very hard to do, which is a good part of the reason why even when Copernicus published his heliocentric model (not a proof, but a new mathematical model) his ideas took decades to become mainstream. If you have a rudimentary telescope / binoculars and know to look, then you can observe that Venus has phases and use that as a basis for argument (as Galileo did), but even then, it's perfectly possible to cook up special models where Venus has phases and the earth is still stationary (see https://en.m.wikipedia.org/wiki/Tychonic_system).
Did Aristarchus of Samos develop a model that made any predictions that could be verified? I think that the ancients thinking about heliocentrism were mostly contemplating it as philosophy. The section you linked doesn't say anything about evidence for heliocentrism, which is what 'jschwartzi is saying was lacking.
Stuff like parallax and Foucault's pendulum isn't obvious until it's already been seen, and AFAIK wasn't investigated until the 17th century.
Indeed for hundreds of years western astronomers predicted the locations of the planets using epicycles and not by calculating orbits assuming a heliocentric system. And it worked! Beautifully! The earth-centric model has excellent predictive power. It explained everything the ancients were aware of.
This is all as a lesson in both humility and in recognizing that our ancestors were not stupid or lacking reason. They just didn't have the tools we have. And for all that the heliocentric seems obvious, remember that it is only obvious because we have been taught it. Our ancestors had been taught an earth-centric model instead, and it was obvious to them.