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The use of hydrogen in transportation is considered a promising solution to reduce CO2 emissions and combat climate change. Among the various technologies, PEM fuel cells represent a consolidated choice for hydrogen propulsion given their lightweight and relatively low cost. However, despite a few cases of successful applications of PEM fuel cells in road and rail transport, there are still barriers hindering the full exploitation of this technology, especially in the aerospace sector. Research is needed to assess the long-term viability, and modeling tools are of utmost importance for this task. The highly complex architectures necessary for hybrid propulsion require new methods for design and optimization, for which accurate but computationally fast models are critical. This paper presents a new methodology of using surrogate-based optimization to assist the design of the power system for a regional electric aircraft. A multi-objective optimization framework has been developed considering the weight, and efficiency of the power system, as well as the operating current density of the fuel cell stack. A surrogate model based on Gaussian Process regression and Singular Value Decomposition is employed to reduce the computational cost. The results show that the surrogate-based optimization approach could accelerate the optimization process without significantly affecting the prediction accuracy. This approach could be used to guide the design of experiments/high-fidelity simulations for the optimal design and energy management of power systems for electric aircraft.