Field evidence from the Pilbara craton (Australia) and Kaapvaal craton (South Africa) indicate that modern tectonic processes may have been operating at ca. 3.2 Ga, a time also associated with a high density of preserved Archaean impact indicators. Recent work has suggested a causative association between large impacts and tectonic processes for the Hadean. However, impact flux estimates and spherule bed characteristics suggest impactor diameters of <100 km at ca. 3.5 Ga, and it is unclear whether such impacts could perturb the global tectonic system. In this work, we develop numerical simulations of global tectonism with impacting effects, and simulate the evolution of these models throughout the Archaean for given impact fluxes. We demonstrate that moderate-size (~70 km diameter) impactors are capable of initiating short-lived subduction, and that the system response is sensitive to impactor size, proximity to other impacts, and also lithospheric thickness gradients. Large lithospheric thickness gradients may have first appeared at ca. 3.5-3.2 Ga as cratonic roots, and we postulate an association between Earth's thermal maturation, cratonic root stability, and the onset of widespread sporadic tectonism driven by the impact flux at this time.