How did Skynet rebuild infrastructure after Judgement Day?

Question

Inspired by this question regarding how Skynet preserved itself during Judgement Day.

It's easy to imagine that Skynet could preserve itself, especially considering it's a military AI that likely has unrestricted access to self-sufficient military datacenters. But, I'd imagine a full global thermonuclear war would destroy mining, refining, and manufacture facilities required to build a something simple as a flashlight, much less an advanced piece of tech like a Terminator.

Any robots that already existed within Skynet's network on Judgement Day would have to be physically altered to shut them down such as they could withstand EMP from the blasts, which means they could not be re-activated remotely. As mentioned in a comment, Reese told Sarah that some humans were kept alive to work, but there'd still have to be a mechanical presence to force the humans to work. Where did Skynet get its initial work force to establish its industrial infrastructure?

Answer 1

As we saw in Terminator 3, the bulk of Skynet's army came from the machine shops under Cheyenne Mountain. These 'terminators' evidently radiated out in the aftermath of Judgement Day (having been kept safe from the EMP due to their hardened military-grade electronics and the sheer bulk of the mountain above them), then established human labour facilities like the Century Work Camp to dispose of the rest of humanity and, presumably to provide the raw materials needed while it established the automated factories that churned out the later model terminators.

REESE: Hunter Killers. Patrol machines. Build in automated factories. Most of us were rounded up, put in camps...for orderly disposal.

...

Some of us were kept alive... to work. Loading bodies. The disposal units ran night and day. We were that close to going out forever...

By the time of Terminator, almost all of the human slaves have been eliminated and, we assume, replaced with (largely radiation-immune) robots to do the same work.

Answer 2

My theory is that humans had already built Terminator models to begin with before Skynet became self-aware. Skynet simply turned on terminators and other machines that roved and flew that were built by man and then programmed these machines to build more of them. Remember in Terminator 3 they had a warehouse full of machines that were robotically intended for defense.