Upon intense femtosecond photoexcitation, a many-body system can undergo a phase transition through a nonequilibrium route, but understanding these pathways remains an outstanding challenge. Here, we use time-resolved second harmonic generation to investigate a photoinduced phase transition in Ca_{3}Ru_{2}O_{7} and show that mesoscale inhomogeneity profoundly influences the transition dynamics. We observe a marked slowing down of the characteristic time τ that quantifies the transition between two structures. τ evolves nonmonotonically as a function of photoexcitation fluence, rising from below 200 fs to ∼1.4 ps, then falling again to below 200 fs. To account for the observed behavior, we perform a bootstrap percolation simulation that demonstrates how local structural interactions govern the transition kinetics. Our work highlights the importance of percolating mesoscale inhomogeneity in the dynamics of photoinduced phase transitions and provides a model that may be useful for understanding such transitions more broadly.