There has been extensive research into the nonlinear responses of the Earth system to astronomical forcing during the last glacial cycle. However, the speed and spatial geometry of ice sheet expansion to its largest extent at the Last Glacial Maximum 21 thousand years ago remains uncertain. Here we use an Earth system model with interactive ice sheets to show that distinct initial North American (Laurentide) ice sheets at 38 thousand years ago converge towards a configuration consistent with the Last Glacial Maximum due to feedbacks between atmospheric circulation and ice sheet geometry. Notably, ice advance speed and spatial pattern in our model are controlled by the amount of summer snowfall, which is dependent on moisture transport pathways from the North Atlantic warm pool linked to ice sheet geometry. The consequence of increased summer snowfall on the surface mass balance of the ice sheet is not only the direct increase in accumulation but the indirect reduction in melt through the snow/ice–albedo feedback. These feedbacks provide an effective mechanism for ice growth for a range of initial ice sheet states and may explain the rapid North American ice volume increase during the last ice age and potentially driving growth during previous glacial periods.