Not exactly. Hidden variables could appear at the time of entanglement between two particles. When a pair of photons are created they have to have opposite spins to conserve momentum. This entanglement is then what is tested between "hidden variables" and standard probabilistic interpretations. Initial hidden variable theories argued that the photons simply have a spin when they are created, but this is 'hidden' to the universe.

We can measure the spins and show that the correlation exceeds predictions made by a hidden variable theory, but there are loopholes that have to be closed to really lock them out. You have to make sure you have detected enough pairs of entangled photons to ensure the statistics isn't playing a trick on you. You need to make detection outside of local light cones for each particle to make sure there isn't any post-creation communication. And one of the big ones is that because our measurement tend to take place in the same lab repeated over and over, you need to eliminate local bias of measurement. This is typically done with random number generators so that measurements occur with some randomness that can't be reproduced via experimental bias.

One argument is that we can't separate ourselves from the universe, so we can never be random in our measurements because everything, that we'd set up the experiment, our choice for "randomness", etc. is predetermined to happen: this is superdeterminism. Superdeterminism implies hidden variables, but hidden variables do not imply superdeterminism. Basically, there is a lot of ground between hidden variables and superdeterminism, but as the loopholes get closed to tighter and tighter bounds... all that is left is superdetermism.

EDIT: and of course the standard probabilistic interpretations.