The Carthaginians supposedly circumnavigated Africa. Upon their return they weren't believed by some because they claimed that the sun rose and set in the opposite sides of the sky, as in fact it does in the Southern Hemisphere. This little detail suggests they at least made it to the Southern Hemisphere.

The Antiquity Historians will have more detail, but just to give you a quick answer, there is a primary document from the 1st/2nd century CE known as the Periplus of the Erythrean Sea, that describes Roman trade routes in the Indian Ocean. It makes mention of trade with places as far away as East Africa, India, and probably China.