We examine the optimal performance of a quantum Einstein refrigerator using an objective function known as the Ecological function. In our model, heat transfer occurs between the working substance—considered as a two-level quantum system—and a blackbody reservoir through photon absorption and emission. We consider that the particles in two-level system follow Maxwell-Boltzmann distribution. We derive analytical results for the coefficient of performance of a quantum Einstein refrigerator. Our analysis explores the performance at optimal value of Ecological function in two distinct regimes: large contact time and short contact time limits. Additionally, we derive analytic expressions for the lower and upper bounds of the coefficient of performance at optimal value of Ecological function for the aforementioned cases. Our analysis reveals several qualitative results of the refrigerator in which the working substance follows Maxwell-Boltzmann distribution.