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.