Structural Health Monitoring (SHM) is essential for ensuring the reliability of structural and mechanical components across various engineering domains. Traditional model-based SHM techniques often struggle with complex systems and the limited availability of accurate physical models. On the contrary, data-driven, model-independent approaches, while simple and fast, frequently lack a comprehensive understanding of system physics and suffer from generalization issues. In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative that leverages both data and physical models. Despite their success in state estimation for structural systems, limited research has focused on inverse applications. A significant challenge in using PINNs for parameter identification lies in their computational demand. To address this, this study proposes a novel integration of Stochastic System Identification (SSI) and Physics-Informed Neural Networks (PINN) for joint input-state-parameter identification in structural systems (SSI-Pi-LSTM). SSI employs statistical analysis and subspace identification techniques to reliably estimate state-space matrices and dominant modal parameters from structural response data. These parameters can then be incorporated into the PINN framework, reducing estimation time and improving accuracy. This combined approach aims to bridge the gap between efficiency and precision in structural parameter identification.