Non‐native plant pests and pathogens threaten biodiversity, ecosystem function, food security, and economic livelihoods. As new invasive populations establish, often as an unintended consequence of international trade, they can become additional sources of introductions, accelerating global spread through bridgehead effects. While the study of non‐native pest spread has used computational models to provide insights into drivers and dynamics of biological invasions and inform management, efforts have focused on local or regional scales and are challenged by complex transmission networks arising from bridgehead population establishment. This paper presents a flexible spatiotemporal stochastic network model called PoPS (Pest or Pathogen Spread) Global that couples international trade networks with core drivers of biological invasions—climate suitability, host availability, and propagule pressure—quantified through open, globally available databases to forecast the spread of non‐native plant pests. The modular design of the framework makes it adaptable for various pests capable of dispersing via human‐mediated pathways, supports proactive responses to emerging pests when limited data are available, and enables forecasts at different spatial and temporal resolutions. We demonstrate the framework using a case study of the invasive planthopper spotted lanternfly (Lycorma delicatula). The model was calibrated with historical, known spotted lanternfly introductions to identify potential bridgehead populations that may contribute to global spread. This global view of phytosanitary pandemics provides crucial information for anticipating biological invasions, quantifying transport pathways risk levels, and allocating resources to safeguard plant health, agriculture, and natural resources.