There are other approaches though. You could, for instance, come up with a cyclical process that visits identical states. This would constrain time in the same way that 6:00 today is the same (from the clock's perspective) as 6:00 tomorrow.
Groundhog Day! It was a good film, but it was science fiction/fantasy. In the real world you can't get every single atom and electron and photon and neutrino to go back to where or how it was. And it would have been a really boring film if Bill Murray had been reset like everybody and everything else. Anyway, sure, you can contrive a clock based on some cyclical subatomic process that revisits identical states, but it's still a cyclical process/change/motion.
Another approach would be to use something that happens without a cause. I'm thinking radioactive decay. While statistically you can put time in there, for an individual particle that will/might/might not decay, causality it broken and you can claim time isn't relevant. (When I reread that, it sounds pretty wooish, but I had some idea going in so I'll leave it.)
I think it's better to say the cause is unclear. There's been talk of decay rates showing seasonal variations suggesting that the solar neutrino flux contributes to "unbalancing" the atom so that it shakes itself apart like an unbalanced flywheel. We were talking about something similar re muon decay on another thread, wherein the magnetic dipole moment and the Einstein-de Haas effect suggests that spin is a genuine rotation. The upshot IMHO is that radioactive decay can be likened to a warehouse full of humming machines with an average lifetime. Some of them break down, and you can estimate the time by counting how many are still going.
You could also localize time to a system that has motion but only a set of finite states. So, for example, you have a bottle filled with a gas that can only reach a finite number of combinations, always returning to a previous "time" when measured only relative to the inside of the container.
I suppose you could, if the bottle of gas was all there was. But it sounds a bit of a stretch for the whole universe.
Which brings up the question, "Is there time in a bottle?"
What's actually in the bottle is gas molecules, and they're moving. But if they're moving very fast, I could ask you to pick up that bottle and say
Is there heat in a bottle?" When you burn your hand and drop it and it smashes on the floor, you know that the answer is yes. It's similar for time. It's an emergent property of motion, but cumulative rather than an average. Slow molecules, cold gas. Fast molecules, hot gas.
My instincts tell me there ought to be time independent functions in physics, but I'm only a layperson, so I can't pull any out to flaunt.
There are, see for example the
time-dependent Schrödinger equation. But I don't think they help much. Look at the gif of the waveforms on the right, and you don't see time flowing, you see things moving. Or not, as the case may be. Only to see something not moving, light has to move to your eye, electrochemical signals have to move around your brain, so you still can't away from motion.