Accurate estimation of confidential annual transaction values between firms is critical for analyzing supply chain vulnerabilities and simulating economic shock propagation, yet it is severely hampered by data scarcity. This study addresses this challenge by proposing a pragmatic and interpretable two-stage hybrid model that synergistically combines Graph Neural Networks (GNNs) for topological feature extraction and a Light Gradient Boosting Machine (LightGBM) for prediction on heterogeneous tabular data. Our primary contribution is the pioneering application of this hybrid model to the critical, yet under-explored, task of firm-level transaction value estimation. We benchmark GNN architectures (GCN, GAT) and conventional models (LightGBM, MLP) on a global firm-level supply network. Our proposed hybrid model, which uses GCN-generated node embeddings as features for LightGBM, significantly outperforms all standalone models. Critically, we demonstrate that this approach serves as a tool to derive novel network science insights from an AI methodology. Our analysis reveals an empirical "information horizon" of approximately five hops within the global supply network, beyond which GNN performance degrades due to over-smoothing. This work provides a robust, high-performing model for a vital economic prediction task, bridging the gap between advanced AI techniques and practical network science applications.