We noticed a man named “John Reese” among the Gold Order soldiers in the Pacific.
His distinctive facial scarring is similar to that of John Connor in “Terminator”.

And,His family name “Rease” is a reference to John’s father, Kyle Reese.

Maybe… For some reason, he has traveled back in time from the 21st century to the 1940s, when there is a war with the machines.
This would also explain why the Enlisted world has had numerous time paradoxes.