This is a little bit off topic, but I read something like this and I think, "Here it comes again." So let me anticipate something.
Some years ago, I went around and around with some people about how low-entropy the early universe was and how could it have started so wound up. Their point, as you can imagine, is that it took an intelligence to design a low-entropy starting universe since low-entropy means "highly ordered."
The only way an unimaginably hot quark-gluon plasma is low-entropy is if it is super-small. It turns out that that's indeed the trick. Within the space available (almost zero), the universe is as high entropy as it can be, a gas so super-hot it doesn't even have baryons, just quarks and gluons.
So, yes, where "order" is set as the inverse of "entropy," then like those pool balls racked in the triangle, the low entropy of the early universe comes from confinement in a small space. (It's a singularity of some sort.) If for some reason that triangular rack is allowed to grow bigger every game, pretty soon the initial game conditions are looking pretty ragged.
But all that is using "order," "disorder," and "entropy" in narrow senses. There's a fallacy of equivocation in thinking this equates to "order" as in keeping your room neat. It most certainly does not.
Even as the total entropy of our universe rose with expansion, also with that expansion the plasma cooled. Baryons formed. Atoms formed. Gas and dust condensed under gravity to form stars and planets. Life arose. The universe is "more disordery" in a limited technical sense of the word. However, in the sense most of us think of it there is more order everywhere and anywhere in the arrangement of matter than existed in the quark-gluon plasma. We're just racked up in a really big, loose rack now.
There are definitely some terminology problems here. Similar, really, to those who say: "Laws of nature? Aha! That means there's a law-giver!"
The increase of entropy since the BB is mostly a decrease of heat and compactness. (No doubt, our resident physicists will point out the many ways that's incorrect.) If being hot and condensed is so "ordered" that it implies a supreme intellect, well, the implication escapes me.
Order is a funny term. It can mean everything quiet and organized, or it can mean uniformity. Uniformity could be the condition in a totally random system as when entropy is maxed out or in a political system where everyone thinks the same.