The fact that atoms exist does not rule out a hidden variable formulation (though for the record such formulations are ruled out by other experiments).
For example the electron wavefunction of a hydrogen atom gives us the probability of finding the electron at any particular point. However the electron could still have a definite hidden position, which would of course be a function of time. As an analogy consider a rubber ball bouncing around at very high velocity in a closed box. We can define a function that gives us the probability of finding the tennis ball at any particular point in the box, but the tennis ball still has a well defined position.
The point is that in the macroscopic case of the tennis ball there is a well defined position, but for the electron in the hydrogen atom the position is simply not defined until we interact with the atom in some way that localises the electron. The position we get is the position at which the electron interacts, not some hypothetical position where it was located immediately prior to the interaction.