The distribution of shear-wave velocities in the subsurface is generally used to assess the potential for seismic liquefaction and soil amplification effects and to classify seismic sites. Newly developed distributed acoustic sensing (DAS) technology enables estimation of the shear-wave distribution as a high-density seismic observation system. This technology is characterized by low maintenance costs, high-resolution outputs, and real-time data transmission capabilities, albeit with the challenge of managing massive data generation. Rapid and efficient interpretation of data is the key to advancing application of the DAS technology. In this study, field tests were carried out to record ambient noise over a short period using DAS technology, from which the surface-wave dispersion curves were extracted. In order to reduce the influence of directional effects on the results, an unsupervised clustering method is used to select appropriate clusters to extract the Green's function. A combination of a genetic algorithm and Monte Carlo (GA-MC) simulation is proposed to invert the subsurface velocity structure. The stratigraphic profiles obtained by the GA-MC method are in agreement with the borehole profiles. Compared to other methods, the proposed optimization method not only improves the solution quality but also reduces the solution time.