Microsoft did implement a not-so-thin POSIX layer and an ELF loader atop the NT kernel, it's WSL1 (Windows Subsystem for Linux). It was obsoleted by WSL2, which uses a specifically-tuned Linux VM instead for performance and completeness reasons.

I haven't played with it, but I think the classic Windows POSIX subsystem used the COFF/PE file formats instead of ELF.