A zero initial velocity of the axion field is assumed in the conventional misalignment mechanism. We propose an alternative scenario where the initial velocity is nonzero, which may arise from an explicit breaking of the PQ symmetry in the early Universe. We demonstrate that, depending on the specifics about the initial velocity and the time order of the PQ symmetry breaking vs. inflation, this new scenario can alter the conventional prediction for the axion relic abundance in different, potentially significant ways. As a result, new viable parameter regions for axion dark matter may open up.