The Pliocene–Pleistocene Transition (PPT), from around 3.2 to 2.5 million years ago (Ma), represented a major shift in the climate system and was characterized by a gradual cooling trend and the appearance of large continental ice sheets over northern Eurasia and North America. Paleo evidence indicates that the PPT was accompanied and possibly caused by a decrease in atmospheric CO 2 , but the temporal resolution of CO 2 reconstructions is low for this period of time and uncertainties remain large. Therefore, instead of applying existent CO 2 reconstructions we solved an ‘inverse’ problem by finding a schematic CO 2 concentration scenario that allows us to simulate the temporal evolution of key climate characteristics in agreement with paleoclimate records. To this end, we performed an ensemble of transient simulations with an Earth system model of intermediate complexity from which we derived a best guess transient CO 2 scenario for the interval from 3.2 to 2.4 Ma that gives the best fit between the simulated and reconstructed benthic δ18O and global sea surface temperature evolution. Our data-constrained CO 2 scenarios are consistent with recent CO 2 reconstructions and suggest a gradual CO 2 decline from 375–425 to 275–300 ppm, between 3.2 and 2.4 Ma. In addition to a gradual decline, the best fit to paleoclimate data requires the existence of pronounced CO 2 variability coherent with the 41-kyr (1 kyr = 1000 years) obliquity cycle. In our simulations the long-term CO 2 decline is accompanied by a relatively abrupt intensification of Northern Hemisphere glaciation at around 2.7 Ma. This is the result of a threshold behaviour of the ice sheets response to gradual CO 2 decrease and orbital forcing. The simulated Northern Hemisphere ice sheets during the early Pleistocene glacial cycles reach a maximum volume equivalent to a sea level drop of about 40 m. Both ice volume and benthic δ18O are dominated by 41-kyr cyclicity. Our simulations suggest that before 2.7 Ma Greenland was ice free during summer insolation maxima and only partly ice covered during periods of minimum summer insolation. A fully glaciated Greenland comparable to its present-day ice volume is modelled only during glacial maxima after 2.7 Ma and more continuously after 2.5 Ma.