The interaction of water with metal surfaces is at the heart of electrocatalysis. But there remain enormous uncertainties about the atomistic interactions at the electrode-electrolyte interface (EEI). As the first step toward an understanding of the EEI, we report here the details of the initial steps of H2O adsorption and complex formation on a Ag(111) surface, based on coupling quantum mechanics (QM) and ambient-pressure X-ray photoelectron spectroscopy (APXPS) experiments. We find a close and direct comparison between simulation and experiment, validated under various isotherm and isobar conditions. We identify five observable oxygen-containing species whose concentrations depend sensitively on temperature and pressure: chemisorbed O* and OH*, H2O* stabilized by hydrogen bond interactions with OH* or O*, and multilayer H2O*. We identify the species experimentally by their O 1s core-level shift that we calculate with QM along with the structures and free energies as a function of temperature and pressure. This leads to a chemical reaction network (CRN) that we use to predict the time evolution of their concentrations over a wide range of temperature (298-798 K) and pressure conditions (10-6-1 Torr), which agree well with the populations determined from APXPS. This multistep simulation CRN protocol should be useful for other heterogeneous catalytic systems.