So… it’s like you completely understand the issue :)
And obviously, you tax the fuel at the source, right when it comes out of the ground. Higher prices get passed down, changing behavior because the products externalities are priced correctly from the start.
To be clear, the source would still be the consumer. Hydrocarbons can be used for non-CO2 emitting purposes such as chemical feedstock for pharmaceuticals, solvents, etc. We should only be levying a tax upon uses that emit CO2 into the atmosphere, i.e. burning them in your ICE vehicle. It’s not the fracking company that’s emitting the CO2 (unless they’re gas flaring or similarly emitting carbon during extraction but this is a rounding error on total emissions).
You can. Everything- including basic things like food, transportation, construction, healthcare- will become more expensive, of course. My objection was to ask fossil fuel companies to pay after you already bought and burned your fuel cheap.