First Light and Assembly of GalaxieS (FLAGS) I: The JWST/NIRCam Number Counts and IGL as Constraints on Galaxy Formation Models

JWST observations have been used in conjunction with SED fitting to infer the physical properties of galaxies throughout cosmic time, revealing tensions with the predictions of theoretical models. However, the biases associated with this process are poorly understood, which limits its true constraining power. We introduce the First Light and Assembly of GalaxieS (FLAGS) series, which will leverage forward modelling to confront models with more reliable direct observables. We describe the consistent processing of NIRCam imaging spanning >1 deg, 2 across 30 independent fields, which can be used to measure the galaxy number counts from 0.9-4.4 mu m. The integrated galaxy light (IGL) is constrained with a certainty of about2.5% at the longest wavelengths, producing novel constraints of 6.92, +0.17, -0.17 and 3.46, +0.09, -0.08 nW,m-2,sr-1 at 2.77 and 4.10 mu m respectively. We compare these measurements with predictions from galaxy evolution models and find that the IGL is an unreliable measure of model performance. Comparing against the number counts directly reveals SC-SAM as the best-performing model (chi squared nu=18.6), with its superior performance relative to SAGE attributed to efficient SNe feedback in low-mass halos. We investigate the impact of systematic photometry and forward modelling uncertainties, confirming that the number counts can be a reliable means of evaluating model predictions and performing simulation-based astrophysical parameter inference in the future.