AMD funded a drop-in CUDA implementation built on ROCm: It's now open-source

At first, it was because Nvidia had a wide variety of highly used cards that almost all support some form of CUDA. By-and-large, your gaming GPU could debug and run the same code that you'd scale up to a datacenter, which was a huge boon for researchers and niche industry applications.

With that momentum, CUDA got incorporated into a lot of high-performance computing applications. Few alternatives show up because there aren't many acceleration frameworks that are as large or complete as CUDA. Nvidia pushed forward by scaling down to robotics and edge-compute scale hardware, and now are scaling up with their DGX/Grace platforms.

Today, Nvidia is prevalent because all attempts to subvert them have failed. Khronos Group tried to get the industry to rally around OpenCL as a widely-supported alternative, but too many stakeholders abandoned it before the initial crypto/AI booms kicked off the demand for GPGPU compute.