Solid sorbent materials present an alternative to liquid absorption technologies for capturing CO2 from flue gas. Among the many possible solid materials classes, metal-organic frameworks (MOF) have been the focus of many studies due to their chemical diversity and customizable porous structure. Metal ions and organic linkers can be combined to form porous structures with diameters ranging from 2-100 Å. The adsorption capacity and selectivity metrics can be optimized by tuning the geometrical and chemical aspects independently. The vast material search space of MOF materials represents a computational challenge for selecting promising candidates for further investigation. Given that existing databases contain ~106 materials in total, it would take a CPU-century to screen them all, even if each material only took 1 CPU-hour. The molecular-level simulation of the CO2 adsorption behavior of each material is but a first step in a workflow that must also consider their expected process-level performance in a realistic scenario. In this work, we build and apply a molecular- to process-level screening framework that includes molecular-level adsorption isotherm simulations, adsorption parameter estimation via isotherm model fits, dynamic process modelling and process optimization. In summary, such an end-to-end computational screening framework, the breadth of materials it can process, the depth of features and properties it can simulate, and the systematic analysis and learning it facilitates, is an invaluable tool for the accelerated discovery of solid sorbent materials for carbon capture.