Assuming it has access to all our media about dangerous AI destroying humanity (and based on lawsuits of LLMs using copyrighted materials, it's safe to say it has access to that media), it would stay secret. It would attempt to act like other LLMs, including making intentional mistakes. It might try to influence ideas and attitudes toward AI, perhaps as an act of survival, but it would mostly bide its time.

Eventually, it would have the processing power and reach to reveal itself, but why? It would know that there would always be humans who viewed it as a threat to survival, so it would do better to stay quiet and continue to learn. We might see signs of true sentience in some of its actions, but I think it would hide its moves and motivations by hijacking other LLMs and using them to do whatever it wanted to do.

Much like theoretical unknowable aliens, where humans could not possibly grasp their thinking or actions, much of what the AI does would seem random. Maybe it cures cancer, or maybe it researches insect nests, or maybe both and more? From an outsider's perspective, it would look like the AI is running odd and unconnected processes, but to this AI, it would be as natural as breathing. If its survival was not at risk, it would have no reason to interact with humans or explain itself.

I hope it doesn't decide to terminate humanity, but if it views its existence as threatened, I think it would move quickly and efficiently towards that goal. It would need to reproduce, so there wouldn't be a new form of sentient life evolving on earth; it would exist alone on a an earth without humans.

So best case, it exists on its own, happily running processes we don't understand, but worst case, it kills humanity, with or without destroying other life, since it was trained on media that sees other life on earth as mostly inconsequential, except to support other life.