The sudden, widespread glaciation of Antarctica and the associated shift toward colder temperatures near the Eocene–Oligocene boundary (∼34 Ma) represents one of the most fundamental reorganizations of the global climate system recognized in the geologic record. This glacial inception and the subsequent evolution of the early East Antarctic Ice Sheet (EAIS) are simulated using a new, coupled global climate–dynamical ice sheet model accounting for the paleogeography, greenhouse gas concentrations, changing orbital parameters, and varying ocean heat transport. Suites of long (105 yr) climate–ice sheet simulations are used to investigate the effects of declining atmospheric CO2, compared to those of the tectonic opening of Southern Ocean gateways and the timing of mountain uplift in the Antarctic interior. In contrast to the established paradigm for the glaciation of Antarctica, which centers on the opening of the Southern Ocean gateways and the ‘thermal isolation’ of the continent, our results show that declining Cenozoic pCO2 may have played the dominant role. First, small isolated ice caps formed on the highest Antarctic plateaus. Then, as a CO2 threshold between ∼3× and 2× pre-industrial level (PAL) was crossed, height–mass balance feedbacks were initiated during orbital periods with cold austral summers, triggering much larger, highly dynamic terrestrial ice sheets. As CO2 continued to decline, these isolated ice caps eventually merged into a permanent continental-scale EAIS. In our model, neither the opening of the Southern Ocean gateways nor mountain uplift significantly affected the timing of the major ice sheet transition, given a scenario of gradually declining CO2 from 4× to 2× PAL over 10 million years around the Eocene–Oligocene boundary.