Geophysical, geochemical, and geological investigations have attributed the stable behaviour of Earth's continents to the presence of their Archean cratonic roots. These roots are likely composed of melt-depleted, low density residual peridotite with high Magnesium number (Mg#), while devolatilisation from the upper mantle during magmatic events might have made these roots more viscous and intrinsically stronger than the convecting mantle.Several conceptual dynamic and petrological models of craton formation have been proposed. Dynamic models invoke far-field shortening or mantle melting events, e.g., by mantle plumes, to create melt-depleted and thick cratons. Compositional buoyancy and rheological modifications have also been invoked to create long-lived stable cratonic lithosphere. However, these conceptual models have not been tested in a dynamically self-consistent model. In this study, we present global thermochemical models of craton formation with coupled core-mantle-crust evolution driven entirely by gravitational forces.Our results with melting and crustal production (both oceanic and continental) show that formation of cratonic roots can occur through naturally occurring lateral compression and thickening of the lithosphere in a self-consistent manner, without the need to invoke far-field tectonic forces. Plume impingements, and gravitational sliding creates thrusting of lithosphere to form thick, stable, and strong lithosphere that has a strong resemblance to the Archean cratons that we can still observe today at the Earth's surface. These models also suggest the recycling of denser eclogitic crust by delamination and dripping processes. Within our computed parameter space, a variety of tectonic regimes are observed which also transition with time. Based on these results, we propose that a ridge-only regime or a sluggish-stagnant-lid regime might have been active on Earth during the Archean Eon as they offer favourable dynamics and conditions for craton formation.