Interior exploration using Seismic Investigations, Geodesy and Heat Transport's (InSight) seismometer package Seismic Experiment for Interior Structure (SEIS) was placed on the surface of Mars at about 1.2 m distance from the thermal properties instrument Heat flow and Physical Properties Package (HP³) that includes a self-hammering probe. Recording the hammering noise with SEIS provided a unique opportunity to estimate the seismic wave velocities of the shallow regolith at the landing site. However, the value of studying the seismic signals of the hammering was only realized after critical hardware decisions were already taken. Furthermore, the design and nominal operation of both SEIS and HP³ are nonideal for such high-resolution seismic measurements. Therefore, a series of adaptations had to be implemented to operate the self-hammering probe as a controlled seismic source and SEIS as a high-frequency seismic receiver including the design of a high-precision timing and an innovative high-frequency sampling workflow. By interpreting the first-arriving seismic waves as a P-wave and identifying first-arriving S-waves by polarization analysis, we determined effective P- and S-wave velocities of v_P = 119⁺⁴⁵_-21 m/s and v_S = 63⁺¹¹_-7 m/s, respectively, from around 2,000 hammer stroke recordings. These velocities likely represent bulk estimates for the uppermost several 10s of cm of regolith. An analysis of the P-wave incidence angles provided an independent v_P/v_S ratio estimate of 1.84^+0.89_-0.35 that compares well with the traveltime based estimate of 1.86^+0.42_-0.25. The low seismic velocities are consistent with those observed for low-density unconsolidated sands and are in agreement with estimates obtained by other methods.