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In the development of microwave-to-optical (MO) quantum transducers, suppressing added noise induced by the optical excitation remains a major challenge. Here we report an integrated superconducting cavity electro-optic circuit based on single crystalline thin-film aluminum nitride of ultralow microwave and optical losses. We demonstrate efficient bi-directional MO conversion at milli-Kelvin temperatures, with near-ground state microwave thermal excitation (n e= 0.09±0.06), despite the peak power of the optical drive exceeding the cooling power of the dilution refrigerator mixing chamber. Our dynamical study further reveals different light-induced noise generation mechanisms and provides crucial guidelines for optimizing electro-optic circuits in future hybrid microwave-optical quantum links.