The emergence of new SARS-CoV-2 variants of concern (VOC) has hampered international efforts to contain the COVID-19 pandemic. VOCs have been characterized to varying degrees by higher transmissibility, worse infection outcomes and evasion of vaccine and infection-induced immunologic memory. VOCs are hypothesized to have originated from animal reservoirs, communities in regions with low surveillance and/or single individuals with poor immunologic control of the virus. Yet, the factors dictating which variants ultimately predominate remain incompletely characterized. Here we present a multi-scale model of SARS-CoV-2 dynamics that describes population spread through individuals whose viral loads and numbers of contacts (drawn from an over-dispersed distribution) are both time-varying. This framework allows us to explore how super-spreader events (SSE) (defined as greater than five secondary infections per day) contribute to variant emergence. We find stochasticity remains a powerful determinant of predominance. Variants that predominate are more likely to be associated with higher infectiousness, an SSE early after variant emergence and ongoing decline of the current dominant variant. Additionally, our simulations reveal that most new highly infectious variants that infect one or a few individuals do not achieve permanence in the population. Consequently, interventions that reduce super-spreading may delay or mitigate emergence of VOCs.