The COVID-19 pandemic affected countries across the globe, demanding drastic public health policies to mitigate the spread of infection, which led to economic crises as a collateral damage. In this work, we investigate the impact of human mobility, described via international commercial flights, on COVID-19 infection dynamics on a global scale. We developed a graph neural network (GNN)-based framework called Dynamic Weighted GraphSAGE (DWSAGE), which operates over spatiotemporal graphs and is well-suited for dynamically changing flight information updated daily. This architecture is designed to be structurally sensitive, capable of learning the relationships between edge features and node features. To gain insights into the influence of air traffic on infection spread, we conducted local sensitivity analysis on our model through perturbation experiments. Our analyses identified Western Europe, the Middle East, and North America as leading regions in fueling the pandemic due to the high volume of air traffic originating or transiting through these areas. We used these observations to propose air traffic reduction strategies that can significantly impact controlling the pandemic with minimal disruption to human mobility. Our work provides a robust deep learning-based tool to study global pandemics and is of key relevance to policymakers for making informed decisions regarding air traffic restrictions during future outbreaks.