The ε182W ages of magmatic iron meteorites are largely within error of the oldest solar system particles, apparently requiring a mechanism for segregation of metals to the cores of planetesimals within 1.5million years of initial condensation. Currently favoured models involve equilibrium melting and gravitational segregation in a static, quiescent environment, which requires very high early heat production in small bodies via decay of short-lived radionuclides. However, the rapid accretion needed to do this implies a violent early accretionary history, raising the question of whether attainment of equilibrium is a valid assumption. Since our use of the Hf-W isotopic system is predicated on achievement of chemical equilibrium during core formation, our understanding of the timing of this key early solar system process is dependent on our knowledge of the segregation mechanism. Here, we investigate impact-related textures and microstructures in chondritic meteorites, and show that impact-generated deformation promoted separation of liquid FeNi into enlarged sulfide-depleted accumulations, and that this happened under conditions of thermochemical disequilibrium. These observations imply that similar enlarged metal accumulations developed as the earliest planetesimals grew by rapid collisional accretion. We suggest that the nonmagmatic iron meteorites formed this way and explain why they contain chondritic fragments in a way that is consistent with their trace element characteristics. As some planetesimals grew large enough to develop partially molten silicate mantles, these enlarged metal accumulations would settle rapidly to form cores leaving sulfide and small metal particles behind, since gravitational settling rate scales with the square of metal particle size. Our model thus provides a mechanism for more rapid core formation with less radiogenic heating. In contrast to existing models of core formation, the observed rarity of sulfide-dominant meteorites is an expected consequence of our model, which promotes early and progressive separation of metal and sulfide. We suggest that the core formation models that assume attainment of equilibrium in the Hf-W system underestimate the core formation time.