"Understanding the dawn of the first galaxies and how their light permeated the early Universe is at the very frontier of modern astrophysical cosmology. Generous resources, including ambitions observational programs, are being devoted to studying these epochs of Cosmic Dawn (CD) and Reionization (EoR). In order to interpret these observations, we propose to build on our widely-used, semi-numeric simulation tool, 21cmFAST, and apply it to observations. Using sub-grid, semi-analytic models, we will incorporate additional physical processes governing the evolution of sources and sinks of ionizing photons. The resulting state-of-the-art simulations will be well poised to interpret topical observations of quasar spectra and the cosmic 21cm signal. They would be both physically-motivated and fast, allowing us to rapidly explore astrophysical parameter space. We will statistically quantify the resulting degeneracies and constraints, providing a robust answer to the question, "What can we learn from EoR/CD observations?" As an end goal, these investigations will help us understand when the first generations of galaxies formed, how they drove the EoR, and what are the associated large-scale observational signatures."