It has been previously proposed that glacial inception represents a bifurcation transition between interglacial and glacial states and is governed by the nonlinear dynamics of the climate-cryosphere system. To trigger glacial inception, the orbital forcing (defined as the maximum of summer insolation at 65° N and determined by Earth's orbital parameters) must be lower than a critical level, which depends on the atmospheric CO.sub.2 concentration. While paleoclimatic data do not provide a strong constraint on the dependence between CO.sub.2 and critical insolation, its accurate estimation is of fundamental importance for predicting future glaciations and the effect that anthropogenic CO.sub.2 emissions might have on them. In this study, we use the novel Earth system model of intermediate complexity CLIMBER-X with interactive ice sheets to produce a new estimation of the critical insolation-CO.sub.2 relationship for triggering glacial inception. We perform a series of experiments in which different combinations of orbital forcing and atmospheric CO.sub.2 concentration are maintained constant in time. We analyze for which combinations of orbital forcing and CO.sub.2 glacial inception occurs and trace the critical relationship between them, separating conditions under which glacial inception is possible from those where glacial inception is not materialized. We also provide a theoretical foundation for the proposed critical insolation-CO.sub.2 relation. We find that the use of the maximum summer insolation at 65° N as a single metric for orbital forcing is adequate for tracing the glacial inception bifurcation. Moreover, we find that the temporal and spatial patterns of ice sheet growth during glacial inception are not always the same but depend on the critical insolation and CO.sub.2 level. The experiments evidence the fact that during glacial inception, ice sheets grow mostly in North America, and only under low CO.sub.2 conditions are ice sheets also formed over Scandinavia. The latter is associated with a weak Atlantic Meridional Overturning Circulation (AMOC) for low CO.sub.2 . We find that the strength of AMOC also affects the rate of ice sheet growth during glacial inception.