I still wouldn't call something "random" unless it truly was, despite appearances, anymore than I'd say we have "free will" if determinism were true but we just didn't know the future and only really have the appearance of free will. I've seen people calculate probabilities based on such things as if things were actually random, but they're not since the natural laws of the universe are in play and things follow those laws, like universal gravitation has molecules reacting in a puddle in some low area rather than anywhere in the wider environment, or electromagnetism and chemistry similarly makes certain combination following those laws and aren't just random ingredients making random arrangements of atoms and molecules. I also wouldn't mistake Nature for cruel when it's more indifferent.
Escaping a minimum may require a push, but that push doesn't have to be deliberate or motivated toward a particular goal. Like an earthquake might separate a population in two, and the changed environment for part of the former group might favor a new mutation that was already in the group, or might arise later. But the earthquake isn't random - it's following geological laws - and there are no cruel intentions on Nature's part, nor any desire to change the environment to favor a new mutation, and nor was the mutation a random occurrence. One may not know all the things "behind the scenes" but that doesn't make them random, or filled with purpose or intent, or moving toward a particular goal. But honestly, all this is well beyond the surface analogy I intended and quite off topic. Analogies are good, but hardly perfect in all regards. Beyond the fact the use of a 24-hour division of the day partially works since it has some objection reasons to prevail (not absolute ones that guarantee its use everywhere, mind you, but some objective ones that favor it and make it work for humans and their physiology, as opposed to ones that are purely arbitrary or actually random).
I still resist the term "Creationism" as you applied it to Star Trek since the term is most often used to describe how the universe came about or all life everywhere arose and not just one, or a smaller group of things. As for Intelligent Design, that "theory" assumes at its core that life is too complicated to have arisen without a creator, but then goes on to erroneously conclude it must therefore have been created by something even more complicated - a living, intelligent designer, and conveniently neglects to mention who designed the intelligent designer. Either at some point in a long string of intelligent designers, leading to the first intelligent designer, there arose one independently and therefore it can happen, contrary to the foundational assumption of the so-called theory, thus disproving it, or it makes a final appeal to some divine creator to make the first intelligent designer, making it just a backhanded form of creationism and therefore a religious belief and not a scientific theory. Yes, in Star Trek some writer did assume an ancient humanoid race seeded many local planets in this one galaxy with their DNA template, thus causing many local races to be humanoid and share enough traits to make interbreeding possible (even if other behind the scene notions suggest it's still harder than a human breading with a chimp, and only with the help of a skilled geneticist is it even possible). So many love children in Trek are just from writers who are fine working more with fantasy than science fiction. Fiction aside, the tiny number of races involved in that story hardly approach the universal claim, let alone a galactic-wide claim, that most creationists or intelligent designers would claim, and thus I'd avoid using those terms, or take exception to their use, lest one too easily read too much into those, too.
Just because some use decidedly better tech than stone knives and bearskins, that doesn't make them divine. The founders, for example, despite what they claim and bred into their servants, weren't gods, and nor were the wormhole aliens gods. Nor is Q, god. Nor was Apollo or Sargon. And anyone taking them as gods is just sufficiently primitive and ignorant enough so they don't understand the difference. Unless, of course, you wish to define God differently than some omniscient and omnipotent being that created the universe and all life in it, etc.
True, the duplicate Earth in Miri probably had a 24-hour day, or the Earths in the mirror mirror universes had them as well. And maybe the planet in the Yang/Coms civilization (The Omega Glory) since they were far older than Earth's history, so in a way, we seem to have copied them rather than them copying us (gasp). But yeah, exactly 24 Earth hours long is about as close to seemingly random as you can get, and I see no reason why an ancient race would even want to use that length, even assuming their home world had that exact period of rotation. There is no valid claim they like to micromanage things - only that they wished subsequent races not to be so desperately lonely like they were growing up all alone in the galaxy. Forcing a 24-hour day on those races does nothing toward that end.
It's true one might fairly assume the UT is translating Kira's Bajoran time to Federation time - which doesn't even necesarily suggest it's a integral number of Earth hours, but only the preference settings for round off error lands on 26 hours and not something like 25.967345 hours. Similarly, they often use multiples of 26, like 26, 52 or 78 (like we use 24, 48, and 72). These could be UT translations rounded off to the nearest earth hour so as to not be exceedingly annoying, like a Vulcan might be.
Vic's use of the DS9 clock seems more likely since he has to make many such scheduled events with the DS9 inhabitants than just that one dinner date for Odo and Kira. And telling Odo what the translation between standard time and military time was doesn't seem like he's making fun, but is genuinely trying to impart information (even though it's probably really the writer reminding an often clueless audience what he means). But it's all speculation - and Memory Alpha won't have any of it (in my experience) since they don't wish to publish fan speculation no matter how many facts from the show you can quote to support it (though I think I've seen enough speculation there on other topics to disprove that, but I'm not a MOD there, so why I think the system is based on 24-Bajoran hours (which are pretty close to 26 Earth hours) doesn't impress them enough to keep the paragraph I wrote about it).
Even in the show, enough numbers are given to demonstrate the Trek Universe is remarkably inconsistent when it comes to warp speeds and distances covered. For example, in Obsession, Kirk chases Moby Vampire Cloud 1,000 light years (which should take approximately 1 year at warp 9), but he does it at slower speeds and in short order. And many other examples like that too numerous to mention will reveal vast inconsistencies in the Trek universe. But I suppose one could argue, like they did for subspace communication speeds) these speeds are not constant, but depend largely on the conditions of space in which one is traveling, (or how many subspace communications relays one has laid between two points). Thus, real time communications between Bajor and Earth apparently happen, despite the 54 light year distance requiring 0.3 hours each way at subspace communication speeds (about 60 x the highest warp speed, or warp 9.999999 whatever). Trust me - don't go looking for consistency from numerous different writers who contributed to the Trek universe, or the actors who played the parts, since such matters are well beyond their concern. Too many things in the Trek universe only make sense if you don't look at them too closely, particularly most anything to do with warp speed, transporters, replicators, or holodecks.
