Graph Neural Networks (GNNs) have emerged as powerful tools for predicting material properties, yet they often struggle to capture many-body interactions and require extensive manual feature engineering. Here, we present EOSnet (Embedded Overlap Structures for Graph Neural Networks), a novel approach that addresses these limitations by incorporating Gaussian Overlap Matrix (GOM) fingerprints as node features within the GNN architecture. Unlike models that rely on explicit angular terms or human-engineered features, EOSnet efficiently encodes many-body interactions through orbital overlap matrices, providing a rotationally invariant and transferable representation of atomic environments. The model demonstrates superior performance across various prediction tasks of materials' properties, achieving particularly notable results in properties sensitive to many-body interactions. For band gap prediction, EOSnet achieves a mean absolute error of 0.163 eV, surpassing previous state-of-the-art models. The model also excels in predicting mechanical properties and classifying materials, with 97.7% accuracy in metal/nonmetal classification. These results demonstrate that embedding GOM fingerprints into node features enhances the ability of GNNs to capture complex atomic interactions, making EOSnet a powerful tool for materials' discovery and property prediction.