But that's my point though. Space travel technology was not 60 years old in the 1960s. Space travel was a new technology that didn't have very strong moats, so even though the U.S. was behind, it could easily catch up. That is equivalent to where quantum computing is today. It has fewer, weaker moats and would take less effort to catch up to the Americans, so Chinese efforts would be better spent there.
1) Quantum computing will only be useful in very niche areas, it's not worth it. Quantum computing cannot replace conventional computers, not in this century, no matter how much resources you pour into it.
2) EUV, like a lot of other very complex technologies, will lift up up other technologies and companies that could be used for many other applications. Becoming forced to make the precision optics/mirrors/lens to the tolerance needed for the EUV machine, also means that you now are able to make extremely good optics/mirrors/lens that can be used for many other applications. Much like how the space race was basically the ICBM race, you got good at rockets because you needed them for nuclear delivery, now you can use them for all sorts of tasks unrelated to their intended goal like landing humans on the moon, or the amount of spinoff technologies that NASA has also produced as a side effect of the hundreds of billion poured into the space age.
3) The lead that the soviets had in the initial stages of the space race huge. America was basically starting from scratch, none of the basic infrastructure was in place, at least China has some presence in the lithography space for years, as small as it is. And what of 2025? Space is mature field, yet nobody has landed on the Moon for 60 years, even America is unable to go back. That's a pretty large moat that America crossed in the 1960s.
4) You are correct that China will be wiser to try different methods instead of just blindly chasing ASML. But that's basically what they are doing. They are trying lots of different methods, from different sources of EUV light, to chiplets and packaging, next generation semiconductor materials other than silicon, photonic chips, electron beam lithography/nanoimprint lithography etc etc.
The one thing I would say is that while China is trying everything, I do wish that they gave more funding into the more unconventional ideas like SSMB EUV or nanoimprint lithography or next generation materials like 2D nanosheets. While they are given funding and being worked on, it's clear that large bulk of research and attention is on the more conventional path that is just trying to replicate ASML and the current state of the entire semiconductor industry.