Collisionless shocks are known as efficient particle accelerators, producing ions with energies above 100 keV at heliospheric shocks, and understood to be the main source of galactic cosmic rays from supernova remnant shocks. Energization is attributed to a diffusive shock acceleration process, however, for this processes to become viable, it is first required that some ions undergo an initial acceleration. How this acceleration takes place has long been a key unsolved issue in shock acceleration theory. Different models have been proposed, but there has until now been a lack of observational validation. Using Cluster spacecraft observations and a hybrid plasma simulation of a quasi-parallel shock, we show that the hybrid model can successfully reproduce the ion velocity signatures observed in the turbulent transition layer upstream of the shock. We study the signatures of ion reflection events, and show that they are characteristic of the first step in the acceleration process. These events develop in regions where the trailing edge of large-amplitude upstream waves intercept the local shock ramp and the upstream magnetic field changes from quasi-perpendicular to quasi-parallel. Here, the reflected ions can escape upstream, however, subsequent wavefronts in the upstream region will sweep the ions back toward the shock, where they gain additional energy. Within three to five gyroperiods, many ions have gained sufficient parallel velocity to escape upstream. The success of this comparison validates the hybrid method for studies of ion acceleration at most heliospheric shocks.