CUDA of 18 years ago is very different to CUDA of today.

Back then AMD/ATI were actually at the forefront on the GPGPU side - things like the early brook language and CTM lead pretty quickly into things like OpenCL. Lots of work went on using the xbox360 gpu in real games for GPGPU tasks.

But CUDA steadily improved iteratively, and AMD kinda just... stopped developing their equivalents? Considering a good part of that time they were near bankruptcy it might have not have been surprising though.

But saying Nvidia solely kicked off everything with CUDA is rather a-historical.