Forward-backward semiclassical dynamics (FBSD) has been shown to offer quantitative descriptions of the short time dynamics of low-temperature fluids. This article aims to correct the major shortcoming of FBSD, namely, its inability to capture dynamical effects of a purely quantum mechanical nature Such as tunneling. To this end, we extend the methodology to a quantum-FBSD scheme, where the evolution along the coordinates of a quantum particle is obtained by quantum propagation subject to a time-dependent potential that is evaluated along classical trajectories describing the solvent, whose phase space distributions are determined by FBSD relations. Numerical tests on a dissipative two-level system show that the quantum-FBSD methodology offers a semiquantitative description of the quenched tunneling oscillations. Therefore, the quantum-FBSD methodology will prove to be useful for simulating the dynamics of proton and electron transfer in condensed phase and biological environments.