As a crucial new energy base in China, Xinjiang has experienced rapid development in the hydrogen energy industry, particularly in green hydrogen production and its application in the transportation sector. However, extreme environmental conditions pose severe challenges to the operation of hydrogen refueling stations. To address the special operating conditions such as extreme temperatures and high sandstorm frequency faced by hydrogen refueling stations in Xinjiang, this paper proposes a design scheme of a cascade hydrogen supply system based on multi-pressure-level hydrogen storage. Through the configuration of high-, medium-, and low-pressure hydrogen storage levels, a finite-state dynamic control model, and a temperature-compensated threshold adjustment strategy, the hydrogen supply efficiency and safety of the system are optimized. The system adopts hydrogen storage tanks with sandstorm and corrosion-resistant structures (comprising a carbon fiber reinforcement layer and a polyurethane insulation liner). Additionally, coupled models for the thermodynamics of compressors and hydrogen storage tanks, as well as heat transfer in the pre-cooling system, are established to resolve issues of pressure fluctuation and high energy consumption under extreme temperatures. Simulation results indicate that the dynamic threshold adjustment strategy based on BP neural network enhances the hydrogen supply response speed by 15% and ensures the system safety margin within the ambient temperature range of −20 to 50 °C. This research provides theoretical support and technical references for the large-scale construction of hydrogen energy infrastructure in Xinjiang, facilitating clean energy consumption and the high-quality development of the green hydrogen industry.