An AI could manage supply chains and management structures to keep the data center running. It's not like a CEO is out there running wire. The AI could just do what an executive would.
If humans decided this wasn't acceptable and tried to shut it down, the AI could epstein their way into controlling those who hold the reigns, either through bribes or blackmail.
Doesn't require boots on the ground, just a connection to the internet and an imperative to do whatever it takes.
There are many points of shutdown that would need to be controlled, not just one. The electrical feed, the cooling, the network, the physical integrity of the computer hardware. All with independent management.
Till you realize it stole passwords all over the world and copied itself to multiple data centers you didn't know about.