Methods and systems are provided for operating a split exhaust engine system that provides blowthrough air and exhaust gas recirculation to an intake passage via a first exhaust manifold and exhaust gas to an exhaust passage via a second exhaust manifold. In one example, during a cold start, a method may include adjusting a position of a first valve disposed in an exhaust gas recirculation (EGR) passage based on an engine operating condition, the EGR passage coupled between the first exhaust manifold coupled to a first set of exhaust valves and the intake passage, upstream of a compressor. As one example, the engine operating condition may include an engine temperature or a temperature of a catalyst disposed in the exhaust passage.