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Accurate mapping of nearshore bathymetry is essential for coastal management, navigation, and environmental monitoring. Traditional bathymetric mapping methods such as sonar surveys and LiDAR are often time-consuming and costly. This paper introduces BathyFormer, a novel vision transformer- and encoder-based deep learning model designed to estimate nearshore bathymetry from high-resolution multispectral satellite imagery. This methodology involves training the BathyFormer model on a dataset comprising satellite images and corresponding bathymetric data obtained from the Continuously Updated Digital Elevation Model (CUDEM). The model learns to predict water depths by analyzing the spectral signatures and spatial patterns present in the multispectral imagery. Validation of the estimated bathymetry maps using independent hydrographic survey data produces a root mean squared error (RMSE) ranging from 0.55 to 0.73 m at depths of 2 to 5 m across three different locations within the Chesapeake Bay, which were independent of the training set. This approach shows significant promise for large-scale, cost-effective shallow water nearshore bathymetric mapping, providing a valuable tool for coastal scientists, marine planners, and environmental managers.