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Using pulsed optical excitation and read-out along with single-phonon-counting techniques, we measure the transient backaction, heating, and damping dynamics of a nanoscale silicon optomechanical crystal cavity mounted in a dilution refrigerator at a base temperature of T_{f}≈11  mK. In addition to observing a slow (approximately 740-ns) turn-on time for the optical-absorption-induced hot-phonon bath, we measure for the 5.6-GHz “breathing” acoustic mode of the cavity an initial phonon occupancy as low as ⟨n⟩=0.021±0.007 (mode temperature T_{min}≈70  mK) and an intrinsic mechanical decay rate of γ_{0}=328±14  Hz (Q_{m}≈1.7×10^{7}). These measurements demonstrate the feasibility of using short pulsed measurements for a variety of quantum optomechanical applications despite the presence of steady-state optical heating.