The EPR argument is that local hidden variables exist. One reason hidden variables were not widely considered was that von Neumann produced an influential but wrong proof that hidden variables, either local or nonlocal, could not exist. The error in the proof was probably known to Einstein and some others, but not the general community. In the 1950s, Bohm produced a nonlocal hidden variable theory that explicitly demonstrated that von Neumann's proof was wrong in a way that could not be corrected. Einstein knew Bohm's hidden variable theory, but it was not the sort he was looking for, since Bohm's theory was nonlocal. Bell later showed that the local hidden variable theory Einstein had hoped for was not possible.Ok. So before Bell came along, what was the excuse to even begin entertaining the idea EPR argument in both cases would not actually hold true?
Although the question of hidden variables is related to EPR and locality, the deeper question that Einstein was trying to address was the issue of reality. The problem is that in quantum mechanics, it is very difficult to consider the wave function "real". In typical quantum mechanics, the outcomes of measurements are real in the usual commonsense way, but the wave function is not necessarily real in that sense, and is just a way to calcuate the probabilities of experimental outcomes. This lack of reality means that QM cannot answer the question of whether the moon is there when we are not looking. So if QM is truly fundamental, it seems difficult to retain our naive notion of reality. But if hidden variables exist, then QM is not truly fundamental, and we don't have to give up our naive notion of reality.