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First-order phase transitions are ubiquitous in quantum materials and often take place as nucleation growth processes, from regions that are perceived as defects in the material. The detailed nature of the defects and their relation with the phase transition are generally not well understood. We investigated the evolution of lattice across the Mott transition in perovskite La_1/3Sr_2/3FeO₃ using coherent nano diffraction. Using an unsupervised K-means clustering method, we revealed the existence of nano regions with tensile strains compared to the average atomic structure. These regions serve as nucleation centers and grow beyond the percolation threshold across the phase transition. We further performed first-principles calculations and confirmed the insulating nature of these nano regions. Our results establish a connection among the atomic lattice structure, nanoscale strain heterogeneity and macroscopic material properties, and provide a pathway toward rational material synthesis and control via strain engineering.