Green hydrogen has been identified as a promising energy carrier in the future energy economy. However, its unique combustion characteristics, especially its propensity to flame flashback, necessitate novel burner concepts. Additive Manufacturing (AM) enables the fabrication of geometrically complex and functionally integrated designs that would be infeasible with conventional manufacturing methods. These capabilities can be leveraged using simulation-based design optimization to generate complex burner designs. A major limitation in burner design optimization is the cost associated with high-fidelity (HF) simulations capable of accurately capturing the combustion-relevant processes. These include the turbulent flow inside complex nozzle geometries, the mixture formation with large density differences between fuel and oxidizer streams, and chemical reactions with heat release. These processes are all decisive for the burner’s performance and must therefore be taken into account. To overcome computational cost limitations, we utilize a multi-fidelity (MF) simulation-based optimization framework that leverages computationally efficient low-fidelity (LF) RANS computations and HF large eddy simulations (LES) of mixing processes inside burner nozzles, combining both in a MF surrogate model. Following work of Vance et al. [1], we construct a targeted fuel-air mixture distribution that promotes stable and safe hydrogen combustion. The optimization objective is to design burner geometries that produce this targeted distribution while respecting constraints imposed by the AM process, such as minimum wall thickness and gap width requirements. We demonstrate the efficacy of this approach by optimizing two burner concepts, showing that the optimized designs achieve the targeted mixture distribution. Also transient mixture characteristics are analyzed and taken into account during optimization. The resulting optimized designs highlight the potential of combining MF optimization with AM to accelerate the development of next-generation hydrogen burners and to support the transition toward a carbon-neutral energy economy.