We investigate the thermalization of a two-component scalar field across a second-order phase transition under extremely fast quenches. We find that vortices start developing at the final temperature of the quench, i.e., below the critical point. Specifically, we find that vortices emerge once the fluctuating field departures from its symmetric state and evolves towards a metastable and inhomogenous configuration. The density of primordial vortices at the relaxation time is a decreasing function of the final temperature of the quench. Subsequently, vortices and antivortices annihilate at a rate that eventually determines the total thermalization time. This rate decreases if the theory contains a discrete anisotropy, which otherwise leaves the primordial vortex density unaffected. Our results thus establish a link between the topological processes involved in the vortex dynamics and the delay in the thermalization of the system.
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