As far as I can remember, datacenters aren’t mentioned in the Terminator movies at all. They did have an idea of a computer system gaining sentience, but it wasn’t a word-guessing program running in a datacenter. Their idea was that it was an advanced chip that gave the computers intelligence.

The story has a fun time loop in it. A terminator went back in time to kill Sarah Connor, who was the mother of the leader of the resistance. The terminator was crushed by a hydraulic press in the Cyberdine Systems factory. This left behind a computer chip from the future. Cyberdine Systems used that to create Skynet, which became self-aware, which eventually resulted in the creation of the Terminators, one of which was sent back in time to kill Sarah Connor. Loop again. (Of course, that’s one of a number of origin stories for Skynet, it seems like each new movie, TV series, RPG or comic book comes up with its own story.)

Anyhow, the point being, the focus of “AI” in the series isn’t datacenters that magically become self-aware. It’s a magic computer chip that has properties allowing something to become self-aware. And, at least in one of the interpretations, it requires a time loop.