The arc breakdown phase in automotive spark-plugs is a sub-microsecond event that precedes the main spark event. This phase is typically characterized by strong non-equilibrium plasma phenomena with high voltage and currents. The nature of the initial breakdown phase has strong implications for the successful spark formation and the electrode erosion/lifetime. There are evidently very few studies that seek to characterize this phase in detail. The goal of this work is to investigate this non-equilibrium plasma arc breakdown phase, using high-fidelity computational modeling. We perform studies using the VizGlow non-equilibrium plasma modeling tool. During the early breakdown phase, the plasma forms thin filamentary streamers that provide the initial conductive channel across the gap. Once the streamers bridge the gap, the plasma begins to transition to a thermal arc. The redistribution of electrostatic potential across the gap during the breakdown phase causes a large electric field intensification near the cathode. This leads to significant ion bombardment on the electrode surface and fast gas heating, both of which can be attributed to electrode erosion.