Your question has a slight flaw, as Atlas carries the sky/heavens and not the earth. It's a common misconception as modern art often does show Atlas holding the earth. In classical times however, Atlas would be depicted holding a celestial sphere, like this statue, on which you can see different Greek constellations. Atlas carrying a sphere thus does not mean the ancient Greeks thought the world was round.

But we know they did believe it was. Pythagoras for example thought that since the circle/sphere was the perfect geometrical shape, the Earth and other planets ought to be spheres. Aristotle derived this from the stars, which in Egypt and Cyprus were different than in Greece.

Perhaps the most famous example though is that of Eratosthenes of Cyrene. He is believed to be the first person to calculate the circumference of the Earth. He came remarkably close too, since his calculations came down to a circumference of 46,100 km, whereas it is now believed to be 40,008 km. He supposedly also calculated the tilt of Earth's axis and the distance between the Earth and the sun.

So the ancient Greeks did think the world was round, but this has little to do with the mythological figure Atlas.