Reaching global net-zero by 2050 requires rapidly scaling low-carbon hydrogen, but deployment is hindered by market uncertainty, high capital costs, and weak supply-demand coordination. This paper examines whether liberalizing international hydrogen and ammonia trade can accelerate deployment and how such policies interact with technological innovation. We develop a hybrid framework combining a global TIMES-based energy-system model (KiNESYS-IFPEN) with a stochastic logistic diffusion model calibrated to historical renewable energy growth under imperfect expectations. We find that trade liberalization alone has limited global impact, and mainly reallocates production geographically: the Middle East, North America, Latin America, and China expand as exporters, while Asia Pacific, Europe and Africa become structural importers. Innovation-driven electrolyzer cost reductions raise significantly global deployment success shifting production toward electrolysis. When policies are combined, innovation dominates, while trade openness reinforces regional specialization. These results underscore the central role of technological progress, credible expectations, and the trade-off between cost-efficient specialization and hydrogen supply security.