Our study presents a spatial-stochastic model for the gene regulatory network (GRN) and the signaling pathway governing cell-fate differentiation during early mouse embryogenesis, specifically at the blastocyst stage. Departing from biophysics-based models of gene regulation, we perform stochastic simulations of the biochemical processes driving early mouse embryogenesis both at the cell and tissue level. Combining these simulations with state-of-the-art AI-aided inference techniques, we successfully parameterize our model, replicating key experimental observations and providing mechanistic insights into the biochemical interactions giving rise to them. Thanks to the stochastic nature of our approach, we quantify the high robustness of ICM specification to various kinds of noise, and provide quantitative predictions for the effects of diverse experimentally testable perturbations. Altogether, we provide a deeper understanding of the intricate mechanisms driving early cell-fate decisions in mouse embryogenesis, highlighting the synergy of local cellular and broader tissue-scale interactions that shape development.