The morphogenesis of single cells depends on their ability to coordinate surface mechanics and polarity. During germination, spores of many species develop a polar tube that hatches out of a rigid outer spore wall (OSW) in a process termed outgrowth. However, how these awakening cells reorganize to stabilize this first growth axis remains unknown. Here, using quantitative experiments and modeling, we reveal the mechanisms underlying outgrowth in fission yeast. We find that, following an isotropic growth phase during which a single polarity cap wanders around the surface, outgrowth occurs when spores have doubled their volume, concomitantly with the stabilization of the cap and a singular rupture in the OSW. This rupture happens when OSW mechanical stress exceeds a threshold, releases the constraints of the OSW on growth, and stabilizes polarity. Thus, outgrowth exemplifies a self-organizing morphogenetic process in which reinforcements between growth and polarity coordinate mechanics and internal organization.