Stresses acting on cold, thick and negatively buoyant oceanic lithosphere are thought to be crucial to the initiation of subduction and the operation of plate tectonics, which characterizes the present-day geodynamics of the Earth. Because the Earth's interior was hotter in the Archaean eon, the oceanic crust may have been thicker, thereby making the oceanic lithosphere more buoyant than at present, and whether subduction and plate tectonics occurred during this time is ambiguous, both in the geological record and in geodynamic models. Here we show that because the oceanic crust was thick and buoyant, early continents may have produced intra-lithospheric gravitational stresses large enough to drive their gravitational spreading, to initiate subduction at their margins and to trigger episodes of subduction. Our model predicts the co-occurrence of deep to progressively shallower mafic volcanics and arc magmatism within continents in a self-consistent geodynamic framework, explaining the enigmatic multimodal volcanism and tectonic record of Archaean cratons. Moreover, our model predicts a petrological stratification and tectonic structure of the sub-continental lithospheric mantle, two predictions that are consistent with xenolith and seismic studies, respectively, and consistent with the existence of a mid-lithospheric seismic discontinuity. The slow gravitational collapse of early continents could have kick-started transient episodes of plate tectonics until, as the Earth's interior cooled and oceanic lithosphere became heavier, plate tectonics became self-sustaining.