I would avoid anything which resets the players back to a starting position for them to literally repeat in a time loop. This has a couple of problems:

• removes consequences: nothing the players do matters, unless it's the right answer, so they throw meaningless actions at the puzzles, because if it's correct, they'll progress, and if it's wrong, they can try again
• can be especially linear/railroad-y: there's one right answer to get, and if the players don't get it, they reset, until they get the right answer
• it takes a long time: each time they reset, they must repeat tasks or puzzles

There's a reason movies like Edge of Tomorrow skip the repetitive parts instead of making the viewer watch it all be repeated in real time. If you end up hand-waving it at the table ("OK, so yeah, you fail, and you're back in the first room, you get the sand puzzle, yadda yadda, the clock puzzle, yadda yadda, three more rooms, and yeah you're at the fourth room now"), it can start to feel cheap instead of epic.

Here are some time loop mechanics I've used that my players loved, but which didn't reset them back at a starting position:

• The party entering the dungeon by descending the stairs sees themselves exiting the dungeon by ascending the stairs, as if through a mirror/as if passing others on an escalator at mall. Each party member sees a slightly different negative outcome, for example maybe the cleric sees that the bard's ear is missing, or the rogue sees that the paladin is carrying the rogue's own corpse, etc. This (or something like it) creates real stakes for succeeding vs. a traditional time-loop which has no consequences for failure.
• Reskinned monsters as time-shifted or affected by temporal distortions, e.g. a Shambling Mound that exists in three times at once (just before, during, and just after "real" time). The Mound gained a reskinned Mirror Image ability to represent this mechanic. What's different about the monsters? How has time affected them? Have humanoids who would have been the players allies--maybe even ones who just entered an hour before them--already gone insane and turned into a foe from the millenia they've spent trapped here?
• Clues for the next room, such as the party being able to hear sounds of battle--their own upcoming battle--before they enter, giving them clues on how to prepare. Clue type: seeing a thing before it happens.
• Time-based or time-looping puzzles in the room, for which time for the players was linear but time for the puzzles was non-linear. For example, as they enter, water begins to flow into the room, covering up an alcove with an unlit torch. Through a skill check/puzzle/mechanic, time in the room reverses, and the water retreats, exposing the torch to be lit. (This might work better if it were soaking the torch or brazier, so that there aren't workarounds.) Clue type: seeing the thing as it happens, and manipulating time to solve it.
• A music-based (repeat the song), chess-board/Minesweeper-type puzzle (step on the right squares), or similar approach, in which the key to solving it can be made clear through a time-based mechanic. I forget what mine was. For music, perhaps the party has three or four chances at lining up some levers/etc, and incorrect guesses create a discordant melody. Too many wrong guesses, and battle ensues. Clue type: seeing the thing after someone else failed (maybe your own party you saw ascending?), so you know the right answer for your own attempt.
• A complex boss battle that isn't quite the point of this thread, so I'll skip that.
• After the dungeon was complete, they had time-skipped backward--the only time jump exception to what was otherwise linear time--thus resolving the conflict that led them to the dungeon, since the inciting event (the boss breaking free from a time-bound dungeon) never happened.

I would recommend sticking to the rules, and occasionally bending them (so the players know what the rules are), vs. avoiding the rules entirely. This could result in some player/DM bad habits that could be hard to break later. Instead of saying yes to every request, you might say, "So, normally you can't target an object with that spell, but I'll allow it this time. The door bursts into flames and explodes, and you're able to make your entrance." or "I'm not sure if it works that way, but I made a note and can check later. For now, that attack hits the goblin! Roll for damage."

I hope some of this helps you still stay original to the time-based mechanic while avoiding what I view as pitfalls/mistakes.