To define appropriate planning scenarios for future pandemics of respiratory pathogens, it is important to understand the initial transmission dynamics of COVID-19 during 2020. Here, we fit an age-stratified compartmental model with a flexible underlying transmission term to daily COVID-19 death data from states in the contiguous U.S. and to national and sub-national data from around the world. The daily death data of the first months of the COVID-19 pandemic was qualitatively categorized into one of four main profile types: "spring single-peak", "summer single-peak", "spring/summer two-peak" and "broad with shoulder". We estimated a reproduction number R as a function of calendar time tc and as a function of time since the first death reported in that population (local pandemic time, tp). Contrary to the diversity of categories and range of magnitudes in death incidence profiles, the R(tp) profiles were much more homogeneous. We found that in both the contiguous U.S. and globally, the initial value of both R(tc) and R(tp) was substantial: at or above two. However, during the early months, pandemic time R(tp) decreased exponentially to a value that hovered around one. This decrease was accompanied by a reduction in the variance of R(tp). For calendar time R(tc), the decrease in magnitude was slower and non-exponential, with a smaller reduction in variance. Intriguingly, similar trends of exponential decrease and reduced variance were not observed in raw death data. Our findings suggest that the combination of specific government responses and spontaneous changes in behaviour ensured that transmissibility dropped, rather than remaining constant, during the initial phases of a pandemic. Future pandemic planning scenarios should include models that assume similar decreases in transmissibility, which lead to longer epidemics with lower peaks when compared with models based on constant transmissibility.