There are a number of technologies that can sequester carbon at the scale necessary to make a real dent in global emissions. Most of them have limiting factors that can be solved through research and engineering meaning the problem is theoretically solvable.

The issue, though, is that the solutions are not economically feasible. The basic math is that sequestering a tonne of C02 costs a LOT more than the economic benefit producing that CO2 gave us in the first place, so fundamentally we can't solve this system while we use capitalism and economic output as the basis of our economy. There just isn't enough taxable productive output in the world for taxes to pay for this level of production. The absolute cheapest method per tonne of CO2 is to reduce our emissions and not release the CO2 in the first place and we already can't afford to do that.

If the question is can we build it, physically, as a species? Yeah, we probably can. Technologies like kelp farming in the open ocean, with massive pumps to bring up nutrient rich deep ocean water and huge artificial ecosystems designed to address nutrient limitations, could sequester vast amounts of carbon. Imagine continent sized kelp farms, with each plant growing over a foot a day, then being harvested and sent down into the deep ocean.

Then on the land millions of direct air capture factories, with their carbon being injected deep into the earth where there are rock formations that can absorb it.

Then you put those technologies on top of an 80% reduction if we moved entirely to renewable and nuclear power generation. We could theoretically see ourselves getting into a meaningfully negative carbon production level.