Fuel cells are true net-zero carbon emission power sources for aircraft, which is highly sensitive to weight. In the initial phase of adapting hydrogen fuel cell systems for aircraft powertrains, preliminary design parameter matching remains premature. An explicit method for the performance optimization of aircraft hydrogen fuel cell powertrain systems and a process of preliminary parameter matching are proposed to address this problem. Performance and weight models of the fuel cell stack and its auxiliaries, the cathode air compressor subsystem, and the cooling subsystem are designed, and system performance at various altitudes and power output levels is calculated. The aircraft flight mission performance is synthesized and considered in the optimization process. The optimization result of system performance and the corresponding design parameters are then graphically illustrated as tern plots. Unlike the traditional iterative preliminary system parameter matching and optimization method, which explores the design space non-directionally and converges to a single local optimal point, the proposed explicit method sweeps the design space globally and obtains a group of design points with acceptable optimality. The system design process is boosted by a compact iterative loop. In the optimization practice, the cruise powertrain specific energy is improved by 6.5%. The relationship between specific system design parameters and system performance is displayed globally by the resulting tern plots. Multiple design guidelines are observed and proposed, and design scenarios are directly obtained from the graphs for further engineering processes.