The cthaeh from the king killer chronicles vs the entire world of Cradle
*cthaeh is given 500 years to prepare and sets events in motion but cannot start violence until 490*Cradle does not know Cthaeh is there to kill them until it has been in world for 500 years*Abidan are not involved
Those are some harsh conditions.
The only advantage Cradle has at this point is that there ARE individuals capable of seeing and manipulating the future. I mean, Elder Whisper already demonstrated the capacity to catch glimpses of the future, and he's pretty low on the overall power scale.
This type of scenario is interesting enough that I was already considering it for the distant future, actually (not the cthaeh, obviously, but some other malicious oracle entity). But if I did, their objective wouldn't be to depopulate Cradle.
Because here's the problem: the cthaeh WOULD be detected before 500 years are up. Some of the people on the top end of the scale would go "Who's that messing with the future?" and go find it to blow it up.
And if it started depopulating Cradle, the Abidan WOULD get involved. I mean, heck, the Abidan are pretty spot-on about any foreign threat messing with Cradle's fate. There's a snake in the nursery; the adults aren't going to ignore it.
HOWEVER, given your conditions...
...it gets pretty interesting.
The first thing the cthaeh is going to realize is that it isn't the only fate-manipulating individual around, and that the others have much greater destructive power. So it's going to have multiple layers of misdirection around it: a proxy oracle to take the blame, a decoy tree, some way to mask its touch on fate, and it would probably limit itself to a very subtle, long-term influence to avoid getting caught.
Then it would make a list of these other precognitive threats and make sure that whatever it did destroyed them first. If it can be the only entity capable of manipulating fate, it wins.
The advantage there is that, while there are millions if not billions (population of Cradle is huge) of sacred artists in Cradle with the ability to see hints of fate, there are only a handful capable of manipulating it. And if the cthaeh can kill them, or even most of them, its chances of success increase significantly.
But it's still playing with fire, because while it is making its own preparations, the native oracles are laying their plans as well. Plus, due to the nature of Cradle's magic system, new threats to the cthaeh can pop up anytime, so it has to account for POTENTIAL precognitives as well.
I think it would probably, in order to mask its own influence and still have the most destructive impact possible, start leading psychotic and murderous individuals to sources of great power. It might even start its own cult around itself, dedicated to killing readers of fate. It would certainly provoke the Dreadgods, leading them to go on four separate destructive rampages, and probably wake as many of the other ancient threats as it could.
There are things buried in Cradle that can affect the global climate, swarms of monsters that multiply endlessly, weapons that detonate living beings directly, curses that make innocents into killers...
All that said, I have difficulty envisioning a scenario in which the cthaeh is able to FULLY destroy Cradle.
In the end, it can't act too directly or it risks discovery, and new threats to its existence can pop up any day. And it's an individual, while Cradle is a massive planet with trillions of people, each of whom are POTENTIALLY capable of growing to the degree that they can threaten the tree.
I think it could easily destroy all civilization and cause thousands of Paths to be forgotten, erasing hundreds of legacies and killing billions of sacred artists. It turns the whole planet into an inhospitable post-apocalyptic wasteland in which only the most hardy can eke out a living.
But eventually, someone is going to kill it.
However, that only works if you go with Kvothe's belief of the abilities of the Cthaeth. If you were to agree with Bast's opinions, Cradle has no chance as the Cthaeth will have already predicted all this and everything that may come of it, and all counters to its schemes, thus meaning that the Cradle inhabitants working to stop it are, in fact, furthering its goals.
Sure, except that it's up against similar beings, so assuming that they're equal is a stalemate.
"It predicted you'd predict it, so it was prepared for your prediction, but you predicted that prediction and prepared a prediction of your own..."
Like a lot of these matchups, you have to assume a reasonably equal scale.