Sodium and potassium are known to be present as neutral elements in the exosphere of Europa. The question of the origin of these alkalis—endogenous or exogenous—remains open. They have been ascribed to exogenous contamination due to volcanism from nearby Io, or the accretion of meteorites and dust. However, these mechanisms fail to fit the observed sodium-to-potassium ratio. Sodium and potassium have also been considered to originate from Europa's putative subsurface ocean, generated by past rock-water leaching. The latter scenario implies a journey of the ions and atoms throughout the ice covering Europa. This raises questions about their stability into the bulk as well as on top of ice. These questions are addressed with first principle periodic solid-state density functional theory simulations describing the relative propensities of sodium, potassium, and calcium for being trapped in the bulk. The evolution of the ionic character of these atoms is followed by means of a topological analysis as they come up to the surface of the ice crust. We find that the metals, almost totally ionized in the ice bulk (net charge ~+0.8) where they are stabilized by ~1 eV or more, recover a quasi-neutrality (net charge ~+0.2) when weakly adsorbed at the surface by ~0.15 eV. Our results are consistent with the assumption that sodium and potassium observed in Europa exosphere come from the sputtering of materials issued from the underlying ocean and exposed by resurfacing events. They also suggest that calcium should be searched for by future missions.