The initiation mechanism of Earth’s plate tectonic cooling system remains uncertain. A growing consensus suggests that multi-plate tectonics was preceded by cooling through a single-plate lithosphere, but models for how this lithosphere was first broken into plates have not converged on a mechanism or a typical early plate scale. A commonality among prior efforts is the use of continuum mechanics approximations to evaluate this solid mechanics problem. Here we use 3D spherical shell models to demonstrate a self-organized fracture mechanism analogous to thermal expansion-driven lithospheric uplift, in which globe-spanning rifting occurs as a consequence of horizontal extension. Resultant fracture spacing is a function of lithospheric thickness and rheology, wherein geometrically-regular, polygonal-shaped tessellation is an energetically favored solution because it minimizes total crack length. Therefore, warming of the early lithosphere itself—as anticipated by previous studies—should lead to failure, propagating fractures, and the conditions necessary for the onset of multi-plate tectonics.