It seems immediately obvious to me from basic physical principles that carbon capture is very unlikely to be the solution.

"There was an old woman that swallowed a fly" comes to mind.

Okay, so let's say it's possible, you build out a shit ton of solar power to provide the energy required to sequester all of the carbon dioxide emitted so far.

This is a properly huge undertaking. Now you've paved over some appreciable fraction of the Earth and done a load of pollution and damage mining stuff to make the panels.

If I ransack your house and throw stuff everywhere it will take you a hell of a lot more work to undo the damage than it took me to cause it. Entropy is a bitch.