Abrupt decadal climate changes during the last glacial-interglacial cycle are less pronounced during maximum glacial conditions and absent during the Holocene. To further understand the underlying dynamics, we conduct hosing experiments for three climate states: Pre-industrial (PI), 32 kilo years before present (ka BP) and Last Glacial Maximum (LGM). Our simulations show that a stronger temperature inversion between the surface and intermediate layer in the South Labrador Sea induces a faster restart of convective processes (32 ka BP > LGM > PI) during the initial resumption of the Atlantic meridional overturning circulation (AMOC). A few decades later, an AMOC overshoot is mainly linked to the advection of warmer and saltier intermediate-layer water from the tropical Atlantic into the South Labrador Sea, which causes a stronger deep-water formation than that before the freshwater perturbation. This mechanism is most pronounced during the 32 ka BP, weaker during the LGM and absent during the PI.