Simple: we aren't.

We can find local optima, but there's no real way to prove a given design is the best of all possible designs. We can only find designs which work and meet the given criteria.

One can prove that a design is correct, but it requires the same class of compute as an LLM to properly simulate. Circuit boards are hellishly complicated once you start simulating EM and RF responses.

As for how a good engineer does this, it's the same way pilots can fly helicopters: intuition. It's a skill built up from lots of reading the rules and theory, and lots of practice. One gets a feel for how the various fields and energies are moving.

Which, when you think about it, is just about how neural nets learn, isn't that neat?

I think the real answer here is that machine learning is absolutely capable of producing satisfactorily correct circuit boards. In principle. But I think the problem space is far too large for today's ML techniques and verification/iteration is just way too expensive. Maybe in another few years, I just don't think we have enough compute for it yet.

Only decades of standards compliance, workmanship training, and experience. Human beings are very good at spotting patterns in noisy jungles, and making rational design tradeoffs.

Auto-routers have been around far longer than even smartphones. Somewhat functional in the trivial problem domains, and always useless where design choices mattered.

Best of luck solving a named problem. =3