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Integrated diffraction gratings offer a compact route to magneto-optical traps (MOTs) for atom cooling and trapping, thus preparing MOTs for future scalable quantum systems. While segmented tri-gratings ensure axial radiation pressure balance, they are limited in optical trapping volume. Planar 2D gratings, though offer larger trapping regions, suffer from low diffraction efficiency and the resulting axial pressure imbalance, necessitating the use of a neutral density (ND) filter to achieve this balance. We present a numerically optimized 2D diffraction grating design that overcomes these limitations and satisfies the required optical conditions for laser cooling, namely, radiation pressure balance, specular reflection cancellation, and circular polarization handedness reversal upon diffraction, thus achieving an optical molasses – a necessary condition in MOT. Using Rigorous Coupled Wave Analysis (RCWA) and a Genetic Algorithm (GA), we design a grating for (_ ^87)Rb grating MOT (GMOT) that achieves a 24% first-order diffraction efficiency, of which 99.7% have the correct circular handedness. These properties enable efficient atom cooling without an ND filter when used with a flat-top beam inside the vacuum chamber. Our design simplifies optical alignment, reduces system footprint, and advances the integration of GMOTs into compact quantum devices.