Based on my research, in general, yes. However if you can store biological matter like algae or the Azolla fern in an anoxic environment, you significantly increase how long you can store it.
If you go read about the Azolla event, this is what is believed to have happened roughly 49 million years ago. Azolla is believed to have been growing in the warm waters of the arctic ocean (either by having freshwater being fed to the area and floating atop the salt water, or by diluting it enough to allow the Azolla to survive, I believe the Amazon does this where it empties into the Atlantic now) and as the generations would die off, they'd sink and reach depths that were anoxic and effectively prevented the bulk of the material to decay.
One avenue I found that shows promise for doing this via another method, would be making biochar in massive quantities, Pacific Pyrolysis is a company that interests me here https://pacificpyrolysis.com/about.html. Some of this you would sell as fertilizer, tilling it into the soil, which would only lock it up relatively short term. Some of it you would store in depleted mines that you can effectively cap, basically doing reverse-coal mining.
Other options exist but nothing that will scale the way we need it, an operation in Iceland shows us that you can at least have a negative-emissions power plant by injecting CO2 into basalt where it converts to carbonates, becoming rock.
Dr. Klaus Lackner at the Center for Negative Carbon Emissions also has some promising research with a polymer. You basically make this 'plastic tree' which garbs CO2 out of the air, it gets trapped in the polymer and you then 'wash' it out with water and capture it in the washing process, of course you still have to do something with that captured gas. Here you could sell some for industrial applications and take the rest and pump it into depleted natural gas and oil operations and then cap it in a sort of reverse mining-process again.
I am far from an expert but I've spent more than 100 hours looking into options this summer and fall and I do not see a currently available solution, that even after several generations of refinement, are workable.
I think we need to get lucky and figure out fusion, and fast, I also think we need a group like Oklo Inc to get their reactor up (it should operate on waste from current fission reactors) which would scale more rapidly. These only really solve coal and natural gas though, there's over a billion passenger vehicles on the planet right now that mostly use petroleum.
I know YC is pretty damn optimistic, I believe Altman said something a few weeks ago at the wired event along the lines of 'we will figure out fusion because we have to' but man, I'm considerably more pessimistic. I think the next 10-50 years are going to be interesting and quite tense.