> at build-time

That's going to be hard.

You're going to need an operating system, redox might work, not sure if it can run rustc yet.

Once you have the operating system you need the hardware, specifically the hardware not to be using C. I'm not sure how I would even go about testing that but even if I had a magic wand I don't think it would be easy to cobble together a computer... and I can't even use particularly exotic hardware because of the limited OS selection.