Since the start of the COVID-19 pandemic, an unprecedented number of genomic sequences of SARS-CoV-2 have been generated and shared with the scientific community. The unparalleled volume of available genetic data presents a unique opportunity to gain real-time insights into the virus transmission during the pandemic, but also a daunting computational hurdle if analyzed with gold-standard phylogeographic approaches. To tackle this practical limitation, we here describe and apply a rapid analytical pipeline to analyze the spatiotemporal dispersal history and dynamics of SARS-CoV-2 lineages. As a proof of concept, we focus on the Belgian epidemic, which has had one of the highest spatial densities of available SARS-CoV-2 genomes. Our pipeline has the potential to be quickly applied to other countries or regions, with key benefits in complementing epidemiological analyses in assessing the impact of intervention measures or their progressive easement.