Tissue patterning coordinates morphogenesis, cell dynamics and fate specification. Understanding how precision in patterning is robustly achieved despite inherent developmental variability during mammalian embryogenesis remains a challenge. Here, based on cell dynamics quantification and simulation, we show how salt-and-pepper epiblast and primitive endoderm (PrE) cells pattern the inner cell mass of mouse blastocysts. Coupling cell fate and dynamics, PrE cells form apical polarity-dependent actin protrusions required for RAC1-dependent migration towards the surface of the fluid cavity, where PrE cells are trapped due to decreased tension. Concomitantly, PrE cells deposit an extracellular matrix gradient, presumably breaking the tissue-level symmetry and collectively guiding their own migration. Tissue size perturbations of mouse embryos and their comparison with monkey and human blastocysts further demonstrate that the fixed proportion of PrE/epiblast cells is optimal with respect to embryo size and tissue geometry and, despite variability, ensures patterning robustness during early mammalian development.