Resistive random access memories (ReRAMs) with a bilayer TaOx/HfO2 stack structure have been shown to possess uniquely promising resistive switching characteristics. However, the key atomistic forming mechanisms and the physical processes that govern the behavior of this kind of device remain to be clarified. Here, we present a detailed analysis of the physical mechanisms underlying its forming at the atomistic level through molecular dynamics (MD) simulations using an extended charge equilibration scheme to describe the effects of applied voltage with the charge transfer ionic potential formalism. The displacement of the tantalum ions was found to be the highest, followed by that of the hafnium ions, in response to a sufficiently high applied voltage across the electrodes, whereas the oxygen ions had a relatively minor voltage-driven response. This led to the formation of a tantalum-depleted, oxygen-rich zone near the positive top electrode acting as the anode and the clustering of oxygen vacancies that nucleated into the filament near the negative bottom electrode, or the cathode. This process resulted in partial shielding of the bulk dielectric from the applied voltage. We found a minimum threshold voltage was required to initiate vacancy clustering to form the filament. Filament growth during forming is attributed to a localized mechanism, driven by thermally activated generation of oxygen vacancy defects, which get stabilized by the local electric fields near the edge of the nucleated filament at the cathode.