Living shorelines as a nature-based solution for climate change adaptation were constructed in many places around the world. The success of this type of projects requires long-term monitoring for adaptive management. The paper presents a novel framework leveraging scientific machine learning methods for accurate and rapid prediction of long-term hydrodynamic forcing impacting living shorelines using short-term measurements of water levels and wind waves in the largest estuary in the U.S. Different from existing data-driven wave prediction models focusing on significant wave heights, this study is focused on the prediction of wave energy spectra in shallow water using winds and tides as the input feature and short-term measurements of wave spectra and water depths as the label. Long Short-Term Memory (LSTM) models were developed using four-month wave measurements in the stormy seasons to predict integral wave parameters and energy spectra for multiple years. The developed models accurately predicted wave heights, peak periods, and energy spectra around the living shorelines, capturing complex wave dynamics, such as wave generation by wind, nonlinear wave-wave interactions, and depth-limited wave breaking in the shallow water of a large estuary. The validated models were then used to determine the long-term wave forcing impacting the living shorelines based on the modeled wave characteristics and spectra. Model results show that the surrogate models utilizing LSTM to predict wave spectra in the frequency domain enable long-term predictions of spectral wave evolution with a minimal computational cost. Our findings provide valuable insights into the efficacy of living shorelines in attenuating wave energy and demonstrate the utility of this approach in assessing the effectiveness of such living shoreline structures.