Structural systems experience gradual deterioration over their lifecycle due to fatigue, corrosion, and micro-cracking, which can compromise performance and safety. Detecting not only the presence but also the progression of such damage is critical for enabling timely interventions and informed decision-making. This work presents an exploratory framework for high-fidelity identification and localization of damage progression using time-indexed deformation measurements. The methodology leverages physics-based modeling and adjoint sensitivity analysis to reconstruct structural parameters that vary both spatially and temporally—such as stiffness or material degradation—using displacement and strain data collected at multiple time points. Unlike the conventional approach that identifies a single structural state, this study considers two strategies for incorporating temporal information: sequential identification, where each state builds on the previously identified state, and a moving window approach, which uses measurements from a defined time window to capture short-term evolution and improve insight into progression. For the moving window approach, the inverse problem is formulated as an optimization task, with each time index corresponding to a distinct material property distribution. Key challenges include the high dimensionality of the parameter space relative to limited measurements and the need for temporal consistency and physical plausibility. To address these, spatial regularization techniques (e.g., vertex morphing) are applied to mitigate ill-posedness, and a monotonicity constraint is introduced to enforce non-increasing material properties over time, reflecting realistic degradation behavior. The current work investigates the feasibility of these approaches and compares their performance in tracking and localizing damage progression through numerical examples. The proposed framework offers a promising direction for next-generation structural health monitoring systems focused on lifecycle performance and proactive maintenance.