Not only Chrono Trigger, but lots of time-travel stories, feature the common trope where some time-travel shenanigans seem to be self-causing (what TVTropes calls a "stable time loop":
https://tvtropes.org/pmwiki/pmwiki.php/Main/StableTimeLoop). Of course, the question is always, "how did things ever get into this paradoxical state in the first place??"
To some extent, questions like this have no answer -- "in the first place" may have no meaning when talking about multiple timelines, and of course at the end of the day it's all just fiction and time travel probably isn't actually possible IRL.
However! In my short story, "Do You Believe In Fate" (see the full details here
https://www.chronocompendium.com/Forums/index.php?topic=14219.0 -- it's about lots of Chrono Trigger's philosophical themes, not just time travel physics), I have Lucca describe a kind of "timeline physics", wherein the events of a stable time loop must be some sort of "local minima" in some kind of extra-temporal causal landscape -- ie, they are "stable" in the sense that they're what you get if you iterate a timeline over and over:
1. go back in time to kill Hitler, thus preventing WW2 and changing the timeline
2. but then a future, different war (launched by the USSR a few years later, perhaps) eventually occurs. somebody from that timeline decides to go back in time to kill [whoever seems responsible for this alternate war] to avert it
3. but maybe killing this other person doesn't actually change the big-picture outcome very much, so you still get a very similar USSR-launched war. and maybe when a person from THIS timeline tries to go back in time to change the past, they consistently fail in their efforts, or they pick the wrong target, so the future hardly changes at all
4. after enough cycles of this, you get a perfectly stable self-causing time loop!
Alternatively, you could also have a local minima that bounces around between 2 (or 3, or 4...) different scenarios, where Scenario A causes Scenario B and in turn B causes A. For example:
A: an evil AI is developed, which starts a nuclear war and takes over the world. A brave resistance leader travels back in time to stop the development of the AI.
B: Thanks to the brave time-traveller, the evil AI is never developed. But now that the world develops normally, no brave resistance leader arises to travel back in time. So if anyone else ever time-travels in this world for any reason, the new timeline will pop back to the situation of Scenario A.
Anyways, this might be an interesting way to think about / critique / analyze time travel stories. It also has some interesting implications about the morality of time travellers' actions -- if you know you are stuck in some kind of mostly self-correcting local minima, you will want to think extra hard about how your plan might end up simply reinforcing the existing timeline, and how you might try to kick things over to an entirely different stable local minima.
Here's the relevant section from my story (which also comes in video form at this link!
https://youtu.be/SQQXScnte2I):
Lucca is probably the expert opinion here. She opened the first time-gate, after all, even if it was an accident while she was trying to make a teleportation device. Since then, she’s spent all her spare time working out equations, trying to figure out as much as possible about how the gates work and what all their time-travel is doing to the world. She has concluded – well, honestly, most of it is way over Crono’s head; Lucca has mostly been talking to Robo lately since he’s the only one who can keep up with all the technical stuff. But Crono remembers right before they were about to make the jump into the deep, prehistoric past. He was afraid –they had all been afraid, even if nobody said it– that whatever they did so many millions of years back, it would probably have huge effects on all future ages. Their families and friends might be totally erased, replaced by an entire alternate history. But then, when they actually did return to the present, that’s not at all what they saw. For all they had done –defeating the Reptites, finding enough Dreamstone to repair the Masamune, recruiting Ayla, and saving the whole Iota tribe– the change in the present was completely undetectable.
All of these time-hopping adventures: to Crono it feels like they occur totally outside the normal bounds of causality, a mischievous meddling in the proper order of events. But Lucca points out that if that was the case, the present should be vastly altered whenever they return from visiting a past age. Instead the differences, if they appear at all, are minor and isolated. She says that the only way this makes sense is if the seemingly original, untouched world we grew up in was actually somehow already altered by our current time-traveling actions. Those actions aren’t changing the world but rather in a sense completing it, because somehow the world has always already been changed by them. So does this mean some other version of myself has already done the things I’m doing right now? Are there an infinite number of Cronos, each fulfilling the same destiny over and over? This is where Lucca starts to roll her eyes. “I mean kind of, I guess,” she starts, “But really that’s totally not the right way to think about it. See, you’re still trying to frame things as the result of a normal process of cause-and-effect –made cyclical because of our time-travel, of course, but still decidedly temporal in the ordinary sense. Really it only makes sense to think of the universe stabilizing itself through causal resonance on some unknown extra-temporal level. All of us time-travelers necessarily exist in such a way that our actions are not only self-causing, but also self-stabilizing in the case of variance, and as for how things got this way in the first place? Well, not through any normal process of revision, but instead via some kind of instantaneous extra-temporal harmonic resonance effect. So yeah, no infinite Cronos.”
And no fate? On the one hand, unlike most people in Crono’s time, Lucca doesn’t believe that a god designed the world to follow a special plan. And despite the drama of their adventure, she definitely doesn’t believe in fated heroes, days of judgement, or destined battles between good and evil. But on the other hand, she does believe that the universe is “deterministic”: if you knew what every particle in the whole world was up to during one particular instant, you’d be able to predict their future movement and interactions perfectly, so you’d know exactly what the whole future would be like. How did the particles happen to get like that, rather than being in some other configuration? Well, Lucca says that the world went through some kind of “extra-temporal settling process” of “self-stabilizing resonance,” which means our particular history is “cradled in some low-energy configuration: at least a local, or possibly global minimum within possibility-space.” Deterministic history – that means the future’s inevitable – settled into a stabilizing minimum – that means things couldn’t have happened any other way. Lucca might not call that fate, but to Crono it at least sounds pretty similar.
