On my reading, to say that the prime mover has random initial conditions would be to say that the laws of the universe are random. Clearly, this cannot be the case. Certainly it wasn't the case with the illustration I gave -- the Rule 110 CA. In that case, Stephen Wolfram stands in the role of the prime mover, specifying the initial condition and the simple rules that, over their evolution, generate both order and apparent randomness -- that is, complexity. Just looking at the later iterations of the evolution, it is impossible to tell what the initial simple rules were.
I'm surprised we are reading from the same text. Prime mover as a cause does not rule out randomness. Wolfram goes into great detail about using random numbers for the initial conditions. I wanted to make that clear before moving on to the rest of your post at #4224.
I gather it all has to do with the ability of earlier iterations to convey information to later states of the system.
Evolution certainly does.
In any case, to the extent that natural selection seems to depend (at least in part) on the preservation of information and its transmission to "later iterations" of the system, perhaps Wolfram's insight that its role may not be the decisive role is analogous to whether we, as observers, "encounter" an island of order or a patch of apparent chaos at any given iteration of the systemic evolution, which is essentially unpredictable.
Wolfram thinks that selection at the level of variation that produces highly complex results is washed out. I can buy that, by the way. Instead, self-organization of random noise can produce highly complex adaptive systems.
We have a fair macroscopic viewpoint of nature. We can see the end results. We can see the obvious order that has emerged. It wasn't until people, like Darwin, actually looked carefully at inheritance and change that the realization set in that random factors are at work. Wolfram repeats that random initial conditions lead to ordered end results.