I did exactly that using an LLM. It may not count as independent depending on how strict you are about that, but then LLMs don't do anything independently.
I wrote a small sample program and expected output, then told the LLM to write a compiler for it in C using LLVM. I subsequently told it to extend the language until it could be used for its own compiler, and rewrite the compiler in the new language. It did.
I don't think that contradicts your point about creativity. A compiler is probably a more mechanical task than a CRUD app is. There's a non-negotiable definition of done and correct.
Designing a language is a creative task of course, and I wouldn't expect an LLM to come up with a novel or ergonomic design on its own. In fact subsequent experiments have shown me that LLMs will consistently ignore terrible ergonomics in a language, never seeking opportunities to add abstraction or beauty.