I think you’re using “chance” as a synonym for “miracle.” If by “chance” you mean to posit an inexplicable, brute fact, then “chance” isn’t part of an explanation. This would put an appeal to chance on part with theism and with the claim that God created the universe by a miracle, God being as inexplicable as what you’re calling chance. (In fact, though, that’s not what “chance” means. Someone wins a lottery by chance or randomness, but that doesn’t mean there’s no deterministic, causal explanation of the result.)
In any case, the underlying question here is whether there’s such a thing as a genuine nonreductive explanation. If we can explain something—as in increase our understanding—only by reducing one thing to something else, that means both theism and so-called “chance” aren’t exactly explanatory.
As you say in your article, this means scientific methods won’t supply an absolute, final explanation since their explanations always posit some other explanans to deal with an explanandum. And that’s what I say, too, in “Atheism and the Endlessness of Explanation.” There I posit a promethean, pragmatic agenda in science to account for that endlessness. Even if there were brute facts in the universe, we’d deal with them “rationally” by adding abstracta, by imagining more levels of reality to enable us to control those facts. This is the heart of methodological naturalism and it’s why scientists don’t settle for miracles.
Regarding the analogy with lotteries, you say the universe formed in a single event, but you say the constants were produced independently. I’m not sure that’s known to be so. If some constants formed after others, they may be causally related to each other, in which case the later ones would be subject to natural, reductive explanations. In so far as the constants resulted directly from the universe’s origin point, they wouldn’t be as independent as the lotteries in the series of improbable wins. The analogy is therefore misleading.
The point about the God of the gaps here isn’t that the naturalist needs to appeal to far-future physics. The point is to admit that much isn’t yet known. It’s the theist who leaps from that ignorance to grandiose pronouncements about what must have caused the universe. By contrast, the naturalist says we’re in the dark on the reason for the constants. It’s a question of living with uncertainty. The theist is uncomfortable without ultimate answers to all of life’s questions. That’s why the theist humanizes ultimate reality and calls it “God.” The naturalist has no need to appeal to the virtual miracle of far-off physics, since he or she can live with uncertainty and doubt.
