The most effective form of carbon capture is to leave it in the ground. We need to stop any form of wacky carbon capture scheme that excuses companies into releasing more of it. This BTW. is exactly what most carbon capture adds up to. Burn a few tonnes of coal and plant a few trees or go to ridiculous lengths of trouble to pump less than a percent of the emissions in some underground cavity. It's a scam and it's the current reality of the industry. You hype it up, get the government subsidies & photo opportunity with the local government stooges and then a few years later it adds up to nothing worth mentioning. The planted forest has wilted away (or burned off), and the vast majority of the carbon that was supposed to go in the ground instead got released into the atmosphere. Australia has a carbon capture facility right next to a brown coal plant. It's beyond cynical if you start looking at the numbers.
The only way of even getting to net zero (never mind negative carbon) is by fixing the economics around the whole topic.
Releasing CO2 needs to be an expensive hobby with extremely low cost alternatives. That removes much more carbon from the equation than the cumulative carbon capture efforts (past, present, and planned future). Better still, it drives companies away from the business of making things worse. We are still subsidizing that even. Just stop doing that.
It actually can work quite fast too. Ten years ago, offshore wind was barely a thing, now it's heading to double digit percentages of energy supply in a lot of places. Same with domestic solar, batteries, etc. EV sales are going through the roof. All of that adds up to CO2 that we leave in the ground. Lots of it. Why is that happening? It's cheaper this way now. Simply accelerating what's already happening here will speed things up.