Suppose that we've observed a dozen randomly chosen ravens and they're all black. We (cautiously) make the obvious inference that all ravens are black. But then we find out that regardless of parental color, newly conceived raven embryos have a 50% chance of being black and a 50% chance of being white, and that they have equal life expectancy in the two cases. When we find this out, we thereby also find out that it was just a fluke that our dozen ravens were all black. Thus, finding out that it's random with probability 1/2 that a given raven will be black defeats the obvious inference that all ravens are black, and even defeats the inference that the next raven we will see will be black. The probability that the next raven we observe will be black is 1/2.
Next, suppose that instead of finding out about probabilities, we find out that there is no propensity either way of a conception resulting in a black raven or its resulting in a white raven. Perhaps an alien uniformly randomly tosses a perfectly sharp dart at a target, and makes a new raven be black whenever the dart lands in a maximally nonmeasurable subset S of the target and makes the raven be white if it lands outside S. (A subset S of a probability space Ω is maximally nonmeasurable provided that every measurable subset of S has probability zero and every measurable superset of S has probability one.) This is just as much a defeater as finding out that the event was random with probability 1/2. It's still just a fluke that the dozen ravens we observed were all black. We still have a defeater for the claim that all ravens are black, or even that the next raven is black.
Finally, suppose instead that we find out that ravens come into existence with no cause, for no reason, stochastic or otherwise, and their colors are likewise brute and unexplained. This surely is just as good a defeater for inferences about the colors of ravens. It's just a fluke that all the ones we saw so far were black.
Now suppose that the initial state of the universe is a brute fact, something with no explanation, stochastic or otherwise. We have (indirect) observations of a portion of that initial state: for instance, we find the parts of the state that have evolved into the observed parts of the universe to have had very low entropy. And science appropriately makes inferences from the parts of the initial state that have been observed by us to the parts that have not been observed, and even to the parts that are not observable. Thus, it is widely accepted that the whole of the initial state had very low entropy, not just the part of it that has formed the basis of our observations. But if the initial state and all of its features are brute facts, then this bruteness is a defeater for inductive inferences from the observed to the unobserved portions of the initial state.
So some cosmological inductive inferences require that the initial state of the universe not be entirely brute.