Effective management of the hydrogen supply chain (HSC), starting with supplier selection, is crucial for advancing the hydrogen industry and economy. Supplier selection, a complex Multi-Criteria Decision Analysis (MCDA) problem in an inherently uncertain environment, requires careful consideration. This study proposes a novel hybrid MCDA framework that integrates the Bayesian Best–Worst Method (BWM), Fuzzy Analytic Hierarchy Process (AHP), and Entropy Weight Method (EWM) for robust criteria weighting, which is aggregated using a game theory-based model to resolve inconsistencies and capture the complementary strengths of each technique. Next, the globally weighted criteria, emphasizing sustainability performance and techno-risk considerations, are used in the TODIM method grounded in prospect theory to rank hydrogen suppliers. Numerical experiments demonstrate the approach’s ability to enhance decision robustness compared to standalone MCDA methods. The comparative evaluation and sensitivity analysis confirm the stability and reliability of the proposed method, offering valuable insights for strategic supplier selection in the evolving hydrogen landscape in the HSC.