Given the narrowness of the initial testing criteria, the SARS-CoV-2 virus spread through cryptic transmission in January and February, setting the stage for the epidemic wave experienced in March and April, 2020. We use a global metapopulation epidemic model to provide a mechanistic understanding of the global dynamic underlying the establishment of the COVID-19 pandemic in Europe and the United States (US). The model is calibrated on international case introductions at the early stage of the pandemic. We find that widespread community transmission of SARS-CoV-2 was likely in several areas of Europe and the US by January 2020, and estimate that by early March, only 1 - 3 in 100 SARS-CoV-2 infections were detected by surveillance systems. Modeling results indicate international travel as the key driver of the introduction of SARS-CoV-2 with possible importation and transmission events as early as December, 2019. We characterize the resulting heterogeneous spatio-temporal spread of SARS-CoV-2 and the burden of the first COVID-19 wave (February-July 2020). We estimate infection attack rates ranging from 0.78%-15.2% in the US and 0.19%-13.2% in Europe. The spatial modeling of SARS-CoV-2 introductions and spreading provides insights into the design of innovative, model-driven surveillance systems and preparedness plans that have a broader initial capacity and indication for testing.