Radiocarbon dating provides the age of organic remains that overly glacial sediments.
The shield is almost entirely buried by the East Antarctic Ice Sheet that has an average thickness of 2200 meters but reaches up to 4700 meters in some locations.
The physics of decay and origin of carbon 14 for the radiocarbon dating1: Formation of Carbon-14.2: Decay of Carbon-14.3: The “equal” equation is for living organisms, and the unequal one is for non-living ones, in which the C-14 then decays (hence the 2).
From: Wikimedia Commons We can indirectly date glacial sediments by looking at the organic materials above and below glacial sediments. Marine geological constraints for the grounding-line position of the Antarctic Ice Sheet on the southern Weddell Sea shelf at the Last Glacial Maximum.
There are over forty such techniques, each using a different radioactive element or a different way of measuring them.
It has become increasingly clear that these radiometric dating techniques agree with each other and as a whole, present a coherent picture in which the Earth was created a very long time ago.