We apply a two-step elastic full-waveform inversion (FWI) to well-site survey (WSS) marine seismic data to estimate high-resolution P-wave (Vp) and S-wave (Vs) velocity models. Our approach combines a first global, genetic-algorithm optimization and a subsequent gradient-based inversion. The broad-band frequency content of the available seismic data makes it possible to extend the frequency range considered in the inversion up to 70 Hz and thus to derive a high-resolution elastic characterization of the shallowest part of the subsurface. The lack of low frequencies and the limited maximum source-to-receiver offset of the WSS acquisition, make the GA inversion particularly crucial as it provides a starting model for the gradient-based FWI that contains the large-medium wavelengths of the seismic velocity field. The following gradient-based FWI yields Vp and Vs models characterized by an improved resolution with respect to the outcomes of GA-FWI. The match between the observed and the predicted seismic data proves the reliability of our predictions.