Polydimethylsiloxane (PDMS) is a prominent material for radiative cooling due to its promising optical properties in the mid-infrared spectral region as well as its fabrication easiness. Even though several works have reported that the mid-infrared emissivity of a PDMS film can be increased by surface modification, there is still room for further enhancement through global optimization. Here, we designed and fabricated the thin PDMS film patterned with two-dimensional gratings to obtain the highest emissivity in the wavelength range from 8 to 13 mu m. A surrogate-model-based optimization was performed, and the optimum structure exhibited the averaged emissivity value of 0.99 in the wavelength of 8-13 mu m, which is the highest value reported to date among polymer-based radiative coolers. For real-world applications, we also developed the fabrication method that is repeatable and applicable for various surfaces using a flexible master mold.