Predicting Olympic medal distributions is an increasingly complex challenge due to globalization and a multitude of dynamic factors influencing national sporting achievements. This study aims to overcome the limitations of existing forecasting approaches by developing a more comprehensive and robust predictive model. To address the intricate task of forecasting Olympic medal outcomes, this research focuses on the development and evaluation of a novel hybrid Spatio-Temporal Graph Convolutional Network and Long Short-Term Memory (STGCN-LSTM) model designed to capture complex inter-country spatio-temporal dependencies and long-term national performance trajectories. The proposed STGCN-LSTM model, further enhanced by a Zero-Inflated Compound Poisson (ZICP) framework, effectively integrates geographical and interactive influences with historical performance data, while adeptly managing the common issue of zero-medal counts; a comprehensive triple validation framework, encompassing historical backtesting, policy shock simulations, and causal inference, confirms the model's predictive accuracy and its capacity to reveal insights into the effects of coaching mobility, event specialization, and strategic resource investment. Consequently, this work delivers a sophisticated, data-driven methodology that not only improves the precision of Olympic medal predictions but also provides a valuable foundation for optimizing sports policies and resource allocation strategies across diverse national contexts.