A method for operating a propulsion system for an aircraft, the propulsion system including a gas turbine engine and a fuel cell assembly, the fuel cell assembly including a fuel cell stack having a solid oxide fuel cell defining an outlet positioned to remove output products from the solid oxide fuel cell during operation, the method including: operating the fuel cell assembly to provide output products to a combustor of a combustion section of the gas turbine engine; and operating the fuel cell assembly, the gas turbine engine, or both such that a pressure within an anode of the solid oxide fuel cell is less than a pressure within a cathode of the solid oxide fuel cell, is less than a pressure within a combustion chamber of the gas turbine engine, or both while operating the gas turbine engine.