> With a single scientific advance that would allow rapid carbon capture from the atmosphere
... and reverse the laws of thermodynamics, too!
Recapturing atmospheric CO2 means working to transform from a high-entropy state to a lower-entropy state. That's not going to happen for free.
So you need to have:
1) A fast efficient carbon-capture mechanism.
2) A way to generate lots and lots of power that doesn't itself produce CO2.
You're not describing a "single scientific advance" as much as you're describing dozens or hundreds of major feats of engineering. I'm not saying it couldn't happen, but I would not bet the planet on it.