The kidney develops through elaboration of ureteric epithelial tubules (the future urinary collecting ducts), stroma, and nephron progenitors in the cap mesenchyme that surrounds each ureteric tip as they branch. Dynamic interactions between these tissues coordinate a balance between ureteric tip branching and nephron formation that sets nephron numbers for life, which impacts the probability of adult disease. How then is this balance achieved? Here we study the geometric and mechanical consequences of tubule tip crowding at the embryonic kidney surface and its effect on nephron formation. We find that kidney surface curvature reduces and tubule 'tip domains' pack more closely over developmental time. These together create a semi-crystalline geometry of tips at the kidney surface and a rigidity transition to more solid-like tissue properties at later developmental stages. New tips overcome mechanical resistance as they branch, expand, and displace close-packed neighbors, after which residual mechanical stress dissipates. This correlates with a changing nephrogenesis rate over the tip 'life-cycle'. To draw a causal link between the two, we mimic a mechanical transient in human iPSC-derived nephron progenitor organoids and find increased cell commitment to early nephron aggregates. The data suggest that temporal waves of mechanical stress within nephron progenitor populations could constitute a clock that synchronizes nephron formation and ureteric tubule duplication after E15. Ongoing efforts to understand the spatial and temporal regulation of nephron induction will clarify variation in nephron endowment between kidneys and advance engineered kidney tissues for regenerative medicine.