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Surface acoustic waves (SAWs) coupled to quantum dots (QDs), trapped atoms and ions, and point defects have been proposed as quantum transduction platforms, yet the requisite coupling rates and cavity lifetimes have not been experimentally established. Although the interaction mechanism varies, small acoustic cavities with large zero-point motion are required for high efficiencies. We experimentally establish the feasibility of this platform through electro- and opto-mechanical characterization of tightly focusing, single-mode Gaussian SAW cavities at $\sim$3.6 GHz on GaAs. We explore the performance limits of the platform by fabricating SAW cavities with mode volumes approaching 6$λ^3$ and linewidths $\leq$1 MHz. Employing strain-coupled single InAs QDs as optomechanical intermediaries, we measure single-phonon optomechanical coupling rates $g_0 \approx 2π\times 1.2$ MHz. Sideband scattering rates thus exceed intrinsic phonon loss, indicating the potential for quantum optical readout and transduction of cavity phonon states. To demonstrate the feasibility of this platform for low-noise ground-state quantum transduction, we develop a fiber-based confocal microscope in a dilution refrigerator and perform single-QD resonance fluorescence sideband spectroscopy at mK temperatures. These measurements show conversion between microwave phonons and optical photons with sub-natural linewidths.