Asked by Marie
Glaciers began in Antarctica around 35 million years ago during a period of cooling climates. As the Antarctic continent drifted south, the Drake Passage opened, allowing the Antarctic Circumpolar Current to become established. This current effectively isolated Antarctica from heat transfer from further north, resulting in cooling. So, with its drift southwards to the South Pole, uplift of the Antarctic Peninsula mountains and the cooling effect of the circumpolar current, glaciers began to form on the mountains of Antarctica. See this article about Antarctic Peninsula Ice Sheet Evolution. The evidence for this mostly comes from offshore drilling programmes.
The Sirius Group provides evidence of ancient glaciation in Antarctica from long ago, up to 15 million years ago. Volcanoes in East Antarctica provide evidence of glaciation in the Miocene (12-15 million years ago).