1) Build enough solar / wind to run your country.
2) Double your build to cover for low production periods.
3) Use the surplus to run Fischer-Tropsch process to convert atmospheric carbon to fuel.
4) Keep building solar / wind until synfuel production exceeds your demand.
5) Export the excess synfuel, use proceeds to build more solar / wind.
6) Once synfuel production exceeds global demand, start stockpiling the synfuel.
7) Keep going until atmospheric carbon hits normal levels.
8) Control global synfuel supply.
The economics of oil: different extraction technologies have a different price-per-barrel. If oil goes below that price, there's no profit in doing the extraction and the oil fields get shuttered to wait for higher prices.
If you can produce synfuel at a cost below an oil field, the oil field gets shut down. Solar has been halving in price every five years, so you might well imagine an inflection point where synfuel mined from the atmosphere with solar power is cheaper than extracted oil. At that point, the synfuel company can start accumulating excess profits and squeezing traditional producers out of the market, while protecting its monopoly by acquiring nascent competition and what traditional producers and oilfields it can.
Atmospheric mining is a zero-sum game: there's a limited amount of carbon dioxide in the atmosphere and you have to stop mining when the CO2 levels fall too low. By mining out all usable atmospheric carbon, the company can eliminate any chance of competition. To add carbon to the atmosphere, the company sells synfuel to users who burn it. The company can then mine the carbon back from the atmosphere using solar.
Because the company earlier used its excess profits to acquire unprofitable oil extractors and oil fields, it also has a source of extra carbon ready to go. As global fuel use increases, more and more carbon needs to be circulated through the atmosphere.
Similar to mining, surface solar is also a zero-sum game. To produce solar, you need land area. Once the land area is in use, it can't be used for more solar. Acquiring the best lands for solar use will make competition difficult, especially at scale.
The end state of the atmospheric carbon mining company is a monopoly over hydrocarbons and solar energy. At the end state, there are no oil reserves left and oil is a just-in-time produced synthetic product. How fast you can burn the oil depends on the speed of the atmospheric mining process. This could reach a point where an amount of oil matching the total amount drilled over the past century is circulated through the atmosphere each year. To prevent losing carbon to oceans, there also needs to be a system to extract dissolved carbon from seawater.
