Citing wikipedia: "...the first confirmed sighting of the continent is commonly accepted to have occurred in 1820 by the Russian expedition of Fabian Gottlieb von Bellingshausen and Mikhail Lazarev on Vostok and Mirny". I wonder why, especially because its location is not so far away from South America.
The existence of a Southern Land was postulated by the Greeks, on grounds of symmetry. Aristotle (Meterologica, II, 5) writes:
The closest historical episode of settlement in the polar region that I can think of is the Norse settlement of Greenland. The differences are striking.
The Norse were a seafaring, agricultural society. They could rely on a (comparatively, see below) advanced political system to support their expeditions. Settlements in Greenland were supplied with local agriculture and trade, and trees were notably growing in the region for them to build and cook. They remained small, because the climate was nevertheless rigid and there weren't many suitable places were to create settlements. Climate change, alongside the arrival of the Inuit people, determined the failure of their colonization attempts.
On the other hemisphere, the only candidate people we can reasonably think of are:
Of these, only the Polynesian had sufficient seafaring abilities to reach Antarctica in great numbers. Coming from Equatorial and Tropical regions, they were unprepared to settle in the harsh (euphemism) climate of Antarctica. Even though in the Medieval Warm Period the climate could have been milder, it was still a challenge for the Norse in Greenland. The Arctic temperatures in turn are milder than those of the antipodal region, so even if there was discovery, most certainly there has been no colonization.
The South American Yaghan people, used simple canoes to travel between islands. Their adaptation to cold does not seem adequate to face Antarctica's climate. (Compare e.g. to Inuit's clothings).
This rules out any previous settlement.
As for the discovery, we must consider that none of these people left written records, so we must rely on oral accounts.
Polynesian oral history relates that a great explorer, Hui-Te-Rangiora, sailing far south of New Zealand around 650 A.D., discovered a “white land”:
from Maori associations with the Antarctic, Turi McFarlane, Canterbury University, 2008
Te Waka o Tamarereti