I'm currently reading Chip Wars and according to the author there were other companies trying to build EUV machines. It seems a lot of them shelved the plans after having ploughed a lot of money into research. ASML stayed the course and bet big on it paying off, which it looks like it has.
That's simply not going to happen for a good few years. Most of the high-end processors that you're buying comes from an ASML machine from various foundries around the world, that makes use of EUV. Other lithography machines made by companies like Canon and Nikon are still stuck in DUV. Heard that Huawei has started to step in this game, and has also enjoyed a breakthrough.