Intel doesn't implement CUDA, but they're working on a CUDA to DPC++ (their parallel programming language) migration tool to make the jump less painful. I've tested some of the NVIDIA samples with it and it seems to do the vast majority of the grunt work, but there are still some sections where refactoring is required. You can find it in the OneAPI base toolkit.
The GPU Ocelot project did exactly that at one point. It's probably a legal minefield for an organized corporate entity though.
One of the big attractions of CUDA is not just the core (programming, API, compiler, development tool) but also the libraries (cuDNN, FFT, cuSignal, … It’s a very long list). These libraries are usually not open source, and can thus not be recompiled even if you have core CUDA support.