Every technology we use today was once a science fiction idea. Robots are made out of all those materials because the industrial infrastructure for producing those materials was already in place before we began working on robotics seriously.
A self-replicating robot would most likely have to be designed around being possible to make with fewer materials, and all the compromises that entails. Certainly we can't do it with today's technology.
We can know it's possible though, because we see living things reproduce themselves. Just as we knew heavier than air flight was possible because we could watch birds doing it.
Biology isn't magic. It's just atoms organized into configurations able to self-copy. It should therefore be possible to do this using different atoms than nature uses. Of course the fundamental self-replicating unit of life is very small. It's possible self-replicating robots will need to be as well.
On the nano scale it would be possible to move individual atoms around, building other nanorobots one atom at a time. This solves all the complex manufacturing challenges you mentioned but comes with all the challenges involved in designing workable nanoscale robots.
Alternatively, if humans self replicate, and humans build mines, factories, power plants and so on, you could just replace humans in that equation with general purpose humanoid construction and repair robots.
So long as they can physically do whatever humans can do, so long as factories exist which produce parts for these robots as well as all of the parts needed for the factory itself, all the pieces are in place for very large, cumbersome mechanical replicators.
It's a solvable problem in other words, the challenge is how to miniaturize it. At any rate, did you read the portion of the article which explores what the outcome of the universe is, in the event that AI or self-replicating robots are impossible?