Photoexcitation by ultrashort laser pulses plays a crucial role in controlling reaction pathways, creating nonequilibrium material properties, and offering a microscopic view of complex dynamics at the molecular level. The photo response following a laser pulse is, in general, non-identical between multiple exposures due to spatiotemporal fluctuations in a material or the stochastic nature of dynamical pathways. However, most ultrafast experiments using a stroboscopic pump-probe scheme struggle to distinguish intrinsic sample fluctuations from extrinsic apparatus noise, often missing seemingly random deviations from the averaged shot-to-shot response. Leveraging the stability and high photon flux of time-resolved X-ray micro-diffraction at a synchrotron, we employed established statistical tools to quantitatively characterize the stochastic behavior of the photoinduced dynamics in a solid-state electrolyte. By analyzing temporal evolutions of the lattice parameter of a single grain in a powder ensemble, we found that the sample responses after different shots contain random fluctuations that are, however, not independent. Instead, there is a correlation between the nonequilibrium lattice trajectories following adjacent laser shots with a characteristic correlation length of approximately 1,500 shots, which represents an energy barrier of 0.4 eV for switching the photoinduced pathway, a value that is close to the activation energy of lithium ion diffusion. Not only does our nonequilibrium noise correlation spectroscopy provide insights for studying fluctuations that are central to phase transitions in both condensed matter and molecular systems, but it also paves the way for discovering novel metastable states buried in oft-presumed random, uncorrelated fluctuating dynamics.