If the Universe has two 'end points', one being the Big Bang, and the other being heat death, is there anything in the laws of physics which forbid a random fluctuation in the heat death state from being the reason for the Big Bang? My thinking is this: we know that moving along the time axis from the Big Bang to Heat Death, the various states of the Universe are separated by probabilistic quantum mechanical events. We also know from experience that moving in the opposite direction, the states are linked deterministically (if we prepare the state of an electron by measuring its spin along the x-axis, we find there is a 50/50 chance that the spin is +/-1/2. But once we make the measurement, we know that the outcome - say +1/2 with total certainty because it happened. If we then make a measurement along the y-axis, we again have a 50/50 chance of +/-1/2 but after the measurement we again know the result with 100% - say -1/2 for the 2nd measurement. But if we run the process in reverse, we know with 100% certainty the outcomes of both measurements because the future state of the Universe contains the information of the previous states). This is depicted in the picture below.
Each point is a possible state of the Universe at a given time. An infinite amount of time after the Big Bang, we end up in a state of Heat Death which looks the same no matter what path was taken. From what I understand, there is no sense of direction for the time dimension in space-time (i.e. in general relativity, all the events on the worldline 'exist' together - there is no 'flow of time', future states only contain the information of previous states). So I'm wondering is: Is there any fundamental physical law that prevents us from concluding that a random fluctuation in the Heat Death state, which would result in one of the infinite number of high entropy states that 'preceded' it, is the 'cause' of the Big Bang and the specific worldline of the Universe we experience (because if there is no sense that something 'happens', but rather all events are simply connected by a world line, if one of those states must exist due to a random fluctuation, then all states causally linked to it must also exist - i.e. trace the specific deterministic worldline back toward the Big Bang and you define the complete unique history of the Universe)?