By saying the universe has an arbitrary state before the Big Bang you're also assuming the universe has _a_ state before the Big Bang. But perhaps the universe had no state at all.
A variable is a piece of memory and always has _a_ value. The value may be arbitrary, the value may be unknowable, but we know at least one thing: that at any point in time a variable has exactly 1 value.
Most values for quantum variables have multiple values at any point in space-time.
That said, even if we assume that the universe had no state prior to the big bang, we can postulate that state to be arbitrary, because it may be 0, it may be 1, or it may be both 0 and 1 at the same time.
A variable is a piece of memory and always has _a_ value. The value may be arbitrary, the value may be unknowable, but we know at least one thing: that at any point in time a variable has exactly 1 value.