Sediment supply to the ocean influences basin-margin growth and reflects upstream landscape evolution, including patterns of sediment routing, denudation, and tectono-climatic perturbations in source areas. Constraining sediment supply is useful for inputs to stratigraphic forward models and for predictions of reservoir presence and quality. Because of the importance of sediment supply, geoscientists have developed various methods to estimate it. Here, we apply Monte Carlo simulation (MCS) to the BQART model that is used to describe an empirical relationship between river catchment paleogeography, climate, and sediment load. We calculate a range of sediment supply from North American source areas to the Gulf of Mexico that suggests an overall decrease in median sediment supply from the late Paleocene to the early Eocene from 404–514 to 144–204 million tons per year, depending on the published paleogeographic model that we used to guide our selection of input variables. Comparison of these estimates with downstream sediment records shows that the subsurface depositional rates are within the 10th–90th percentile range of this BQART-MCS uncertainty model. The 50th percentile values of BQART-MCS results are overall larger than the published Wilcox sediment volume, which indicates that the size of Wilcox deep-water fans might be underestimated. We use source-of-change analysis to show the influence of each river-catchment input of the BQART model on change in sediment supply from the late Paleocene to the early Eocene. Integration of empirical-based methods, such as BQART, with physics-based experimental and modeling approaches might provide better constrains on sediment supply and deposition in frontier areas of oil and gas exploration.