Robust full-field response estimation in structural dynamics from sparse sensor measurements remains challenging, especially when responses exhibit high-frequency content or stiff transients [1]. Purely data-driven approaches often demand extensive training data across diverse loading conditions, while standard Physics-Informed Neural Networks (PINNs) can suffer from spectral bias and optimization instability in such regimes [2]. In this work, we propose a physics-guided hybrid FEM–ML framework that combines an equation-of-motion-based finite element model with a data-efficient learning module for full-field dynamic state estimation under sparse sensing. The framework employs two complementary mechanisms. First, low-fidelity FEM-derived global operators—mass, damping, and stiffness matrices are embedded into the learning pipeline to enforce physical consistency and stabilize inference. Second, we introduce a Local Solution Operator trained in a one-shot manner using a single high-fidelity reference simulation. By exploiting the locality of spatial–temporal derivatives, the operator learns the underlying differential operator behavior and functions as a physics-informed interpolator that propagates information from measured sensor locations to unmeasured regions. The proposed framework is validated on numerical structural dynamics problems. Results show that the method achieves accurate full-field response reconstruction using only sparse sensor inputs and a single training instance, outperforming conventional data-intensive baselines while maintaining stable performance in challenging dynamic regimes. These findings suggest a practical and data-efficient pathway for full-field structural response estimation in data-scarce engineering applications.