Also consider the speed of light is also the speed of causality. If there was no such limit it means it would be possible for effects to precede causes which would lead to a very different kind of universe!
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No matter how fast an effect propogates, it is always after the cause (with an infinite speed, I guess effects happen instantaneously, but not before).
Of course, this doesn't fit with a universe described by general relativity, where time can be different for different observers. But you wouldn't have a universe described by general relativity without that constraint in the first place.
I can't think of anything purely in the physical plane, though there's this:
https://en.m.wikipedia.org/wiki/Retrocausality
But if one includes metaphysics, one example (there are others) is an individual's anticipation of another individual doing something in the future could cause them to act in the present.
This is quite the stretch on its own, but if you include this (which exists, as much as people don't like to admit it depending on the context):
https://en.m.wikipedia.org/wiki/Consensus_reality
...it is possible, in that it comes down to the question of is it true that the effect proceeded the cause, and if enough people believe something is true, it is true. And if you disagree, observe human behavior for a while and see for yourself - people will tell you it is true with absolute sincerity, and they often will act in the physical plane based upon that "truth". Wars are started over "not true" "truths", perhaps even all of them.
And if that's not enough, another route is perhaps people really can see the future. People with absolute sincerity tell me they can constantly. Perhaps they are hallucinating (they swear to me they are not), but perhaps they are not, maybe it is yet another thing that science has yet to discover, or cannot discover due to non-determinism, non-falsifiability, consensus reality (a theory cannot be(!) true unless there is consensus agreement that it is true), etc.
Please don't shoot the messenger.