Mercury's crust is mostly the result of partial melting in the mantle associated with solid-state convection. Large impacts induce additional melting by generating subsurface thermal anomalies. By numerically investigating the geodynamical effects of impacts, here we show that impact-generated thermal anomalies interact with the underlying convection modifying the source depth of melt and inducing volcanism that can significantly postdate the impact depending on the impact time and location with respect to the underlying convection pattern. We can reproduce the volume and time of emplacement of the melt sheets in the interior of Caloris and Rembrandt if at about 3.7-3.8 Ga convection in the mantle of Mercury was weak, an inference corroborated by the dating of the youngest large volcanic provinces. The source depth of the melt sheets is located in the stagnant lid, a volume of the mantle that never participated in convection and may contain pristine mantle material.