This study analyzed a recuperative burner system that is critical for energy efficiency and pollutant reduction in the firing processes required in the manufacturing industries. We aimed to optimize the operating conditions of a recuperative burner using computational fluid dynamics (CFD) combined with a novel reduced-order deep-learning technique. The Reynolds-averaged Navier–Stokes model and finite-rate/eddy-dissipation models were used to generate reliable CFD simulation results considering four operating conditions (temperature and mass flow rate of air and fuel). We first validated the CFD model with two-dimensional axis-symmetric experimental burner results and created a proper orthogonal decomposition transformer model using large-scale snapshots of the CFD results and various operating conditions. Subsequently, a genetic algorithm was employed to find the optimal conditions for five different objective functions: fuel economy, decrease in carbon monoxide emissions, reduction in nitrogen oxide emissions, decrease in carbon dioxide production, and an all-encompassing view of the four objectives. Finally, by comparing our proposed approach with previous methods, we confirmed that the obtained optimal operating conditions improve the performance of the recuperative burner. This study provides an optimized framework for recuperative burners to reduce environmental pollution, with potential applications in many industries, such as ceramics, steel, and batteries.