The resource really isn’t the carbon itself but it’s stored chemical energy. Without new energy input, the carbon in CO2 will never become a hydrocarbon again.
Photosynthesis turns carbon and energy into plants immediately.
Longer term the same processes that turned algae and other life forms into oil are still happening and try as we might we aren't going to stop them, but they proceed at what is likely a pace that will take long after humans are extinct to replenish what we have used.
> Longer term the same processes that turned algae and other life forms into oil are still happening
This is unfortunately not true.
The vast majority of our fossil fuels are formed from carbon that was sequestered into cellulose in plants, before anything had evolved the ability to digest cellulose. It piled up, and eventually compressed into coal. Look up the ʾCarboniferous Period" for more details.
These reserves are no longer being formed because we have fungi that break down these materials and return the CO2 to the air.
Planet Earth will never again have oil and coal reserves of the size it did 200 years ago.
While this is true for coal, algae can still form oil. Oil is primarily formed by organic material dumped out by river deltas that are sealed by their sea drying up. That is why places like the Gulf of Mexico are so oil rich. Seabeds are pretty much organic sludge which can be sealed in by salt, and then compressed and heated into oil.
