Carbon capture and storage (CCS) plays an essential role in global decarbonization. Scaling up CCS requires accurate and high-resolution modeling of the storage reservoir pressure buildup and the gaseous plume migration. However, such modeling is very challenging at scale due to the high computational costs of existing numerical methods. This challenge leads to significant uncertainty in evaluating storage opportunities which can delay the pace of global CCS deployments. We introduce a machine-learning approach for dynamic basin-scale modeling that speeds up flow prediction nearly 700,000 times compared to existing methods. Our framework, Nested Fourier Neural Operator (FNO), provides a general-purpose simulator alternative under diverse reservoir conditions, geological heterogeneity, and injection schemes. It enables unprecedented real-time high-fidelity modeling to support decision-making in basin-scale CCS projects.