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Abstract Integrated optomechanical systems are a leading platform for manipulating, sensing, and distributing quantum information, but are limited by residual optical heating. Here, we demonstrate a two-dimensional optomechanical crystal (OMC) geometry with increased thermal anchoring and a mechanical mode at 7.4 GHz, well aligned with the operation range of cryogenic microwave hardware and piezoelectric transducers. The eight times better thermalization than current one-dimensional OMCs, large optomechanical coupling rates,g₀/2π  ≈  880 kHz, and high optical quality factors,Q_opt = 2.4 × 10⁵, allow ground-state cooling (n_m = 0.32) of the acoustic mode from 3 K and entering the optomechanical strong-coupling regime. In pulsed sideband asymmetry measurements, we show ground-state operation (n_m < 0.45) at temperatures below 10 mK, with repetition rates up to 3 MHz, generating photon-phonon pairs at  ≈ 147 kHz. Our results extend optomechanical system capabilities and establish a robust foundation for future microwave-to-optical transducers with entanglement rates exceeding state-of-the-art superconducting qubit decoherence rates.