The key that ultimately made it possible was the light source, and ASML is the only company that sells these light sources. ASML didn't invent the light source entirely on its own; there were a lot of ideas for light sources floating around and the only one that turned out to work was laser-induced plasma from tin microdroplets, which sounds completely crazy but it works [0]. ASML perfected that process (with -- to be fair -- some investment from Intel).
[0] https://www.asml.com/en/technology/lithography-principles/li...
Intel did fight EUV with a technology called SAQP which ultimately turned out not to work as well as EUV, but they were researching EUV at the same time. Here are some more historical articles about Intel's work on EUV in the past. Note the dates.
https://newsroom.intel.com/news-releases/intel-achieves-majo...
https://semiengineering.com/why-euv-is-so-difficult/
https://www.eetimes.com/intel-developing-euv-pellicle/
https://www.extremetech.com/computing/276376-intel-reportedl...