Capture CO2 as biomass or with direct air capture. Pyrolyze biomass to charcoal or use the Bosch reaction to recover pure carbon from CO2 chemically [1]. Then combine the carbon with silicon to form silicon carbide via the Acheson process:
https://en.wikipedia.org/wiki/Acheson_process
Silicon carbide is extraordinarily resistant to mechanical erosion, oxidation, or any kind of natural degradation. Put the silicon carbide in a geologically stable desert and it could keep the carbon out of the carbon cycle until the sun grows hot enough to render the Earth uninhabitable. Continually extract and convert CO2 from the atmosphere and oceans until natural CO2 levels drop near zero and the desert is full of silicon carbide mountain ranges.
As a mere mitigation for AGW, this is a stinker. It requires an order of magnitude more energy and complexity than direct air capture of CO2 (which itself is already too energetically demanding and complex). But if you have the Sahara-sized robotic solar farm and industrial complex to put it into practice, it makes a great doomsday weapon!
Most actually-buildable doomsday weapons leave numerous survivors behind. Ordinary global nuclear war would barely deplete uncontacted tribes in the Amazon. Cockroaches would still survive cobalt salted nuclear warfare at the gigaton scale. Even an army of roving Terminators might eliminate multicellular life yet struggle to locate protozoans.
But I think that Total Carbon Sequestration could end all life, not just the visible-to-the-naked-eye species. All life needs carbon. And no species (save humans, via technological means) is capable of extracting carbon from silicon carbide. So with a hundred trillion dollar investment in a fully autonomous complex of solar farms, carbon capture facilities, and silicon carbide factories, I believe that we could solve global warming and end all life on Earth. Just like the Earth will do naturally in about a billion years [2] as CO2 levels fall, but up to 10,000 times faster! I'm still working on a funding model and a rationale for why this should be done at all, but some things are inspiring just because they're possible.
[1] https://en.wikipedia.org/wiki/Bosch_reaction
[2] https://en.wikipedia.org/wiki/Timeline_of_the_far_future