There is a tiny problem with that hypothesis - there are I think at most 3 potentially viable climate reversal options - DAC, sun shield and aerosol injection in the atmosphere. All 3 options are likely cost through the nose and will require sums and efforts on a global scale. Any single country attempting them on its own, would require to set aside double digit amounts of its GDP for decades, effectively crippling itself economically, while the world passes them by. And all option would require decades, if not centuries of constant work because we don't have any meaningful net negative DAC tech, we don't have any sun shield expertise outside of the JWST and a few small science experiments, and we don't have the required planes to seed atmosphere and neither they are net negative yet. By we I mean both whole globe or any single country.
Game of chicken. Wait as long as you can because as it starts to get worse for everyone, maybe more and more countries will join in on the efforts.
I don't know if any country has the industrial base to do it yourself, as you say, but if any does, it's almost certainly China just due to manufacturing output and expertise alone. They're, what, 30-35% of the world's output? Set aside 30% of that and they can still feed a lot of exports to other countries - more than anyone else - to bring in money. And nobody else has anything close to the leading-edge hands-on know-how to build all the stuff that would be required. As you mention, there's a lot nobody has yet. So the country best at building cutting-edge hardware is gonna have the head start.
If you're a western pessimist, that whole mega-project could easily unlock even more manufacturing, materials science, etc, progress that could be applied to the rest of their output too, furthering the gap between them and everyone else. (But I guess if they did single-handedly save however many billion people from displacement, and the majority of developed countries from massive crisis/invasion/etc, that's probably the least of our worries!)