Yes, but we should be careful here.

Aristarchus had an incredible idea that was well ahead of its time, but he didn't reach the conclusion of heliocentrism based on careful calculations or observations. Quite the opposite; He fully supported the Ancient Greek model of epicycle orbits of the known planets, and like Copernicus many hundreds of years later, was attempting to map the epicycular orbits of the planets onto the perfect Platonic solids.

His reasoning that the Sun was at the centre of the Universe was the result of the same thought process that all Ancient Greek natural philosophers engaged in; What was the cosmic hierarchical order of the five basic elements (Earth, water, air, fire, and quintessence)?

All of them had concluded that quintessence was at the top of the hierarchy, and so it surrounded and permeated all things. It was the crystalline medium of the Cosmos in which the fixed stars were embedded.

The disagreements came from deciding the order from there. The Aristotelean School put Earth next, so the Earth was given the dominant position in the Cosmos. Thales of Miletus also placed the Earth at the centre, but that was because he believed the Earth was composed almost entirely of water, and water was the second in the hierarchy after quintessence. Aristarchus placed fire as the next below quintessence, and so he concluded the Sun was at the centre of the Cosmos.

We must understand that Ancient Greek natural philosophers largely did not conclude results through careful measurement or practical demonstration, but instead took existing models and modified them to fit their own personal biases and conclusions. The epicycle model of the Solar System was particularly useful in these regards because if the movement of the planets didn't match one's predetermined conclusions, one could merely posit that there were greater or fewer epicycular movements of the planets when they dipped below the horizon, the Ancient Greeks being unable to view their orbital paths from the Southern Hemisphere.

The reason you've learned about and remembered the times when the Ancient Greek natural philosophers did use careful measurements and practical demonstrations, like Archimedes weighing King Hieron's crown, or Eratosthenes measuring the circumference of the Earth, is because those discoveries were the exception to the rule.