Computing an equilibrium in congestion games can be challenging when the number of players is large. Yet, it is a problem to be addressed in practice, for instance to forecast the state of the system and be able to control it. In this work, we analyze the case of generalized atomic congestion games, with coupling constraints, and with players that are heterogeneous through their action sets and their utility functions. We obtain an approximation of the variational Nash equilibria-a notion generalizing Nash equilibria in the presence of coupling constraints-of a large atomic congestion game by an equilibrium of an auxiliary population game, where each population corresponds to a group of atomic players of the initial game. Because the variational inequalities characterizing the equilibrium of the auxiliary game have smaller dimension than the original problem, this approach enables the fast computation of an estimation of equilibria in a large congestion game with thousands of heterogeneous players.