What we call crude oil is essentially a complicated reservoir of hydrocarbons plus sulfur-, nitrogen-, oxygen-containing compounds and trace materials. We therefore don't necessarily need to reproduce geological crude oil molecule-for-molecule. We can manufacture the useful hydrocarbon fractions instead.
A particularly interesting architecture would be:
CO₂ + H₂O + energy → H₂ + CO → synthetic hydrocarbons → fuels / lubricants / chemical feedstocks
CO₂ could come from industrial exhaust or direct-air capture. Water provides hydrogen through electrolysis. Renewable or nuclear electricity supplies the energy. CO₂ and hydrogen can then be converted into synthesis gas and subsequently into longer hydrocarbon chains using processes such as Fischer–Tropsch synthesis.
The important distinction is that I'd approach your idea as “artificial resources” rather than merely “synthetic fuel.” Imagine an industrial system where we manufacture substitutes for resources normally extracted from geology:
Artificial Oil → hydrocarbons, lubricants, polymers, chemical feedstock
Artificial Gas → methane or other gaseous energy carriers
Artificial Carbon → graphite/carbon materials from captured CO₂
Artificial Minerals → engineered materials replacing scarce geological inputs
For artificial oil specifically, I think an interesting research target would be something like an Artificial Crude Oil (ACO): not just gasoline or diesel, but a deliberately engineered liquid hydrocarbon mixture that existing refineries could fractionate using much of their current infrastructure.
The chemistry is achievable. The difficult part is the energy and economics. If one tonne of synthetic oil requires so much electricity that extracting conventional petroleum remains dramatically cheaper, it won't replace petroleum. But if electricity becomes sufficiently abundant and inexpensive, carbon becomes recyclable feedstock rather than something humanity has to continuously dig out of the ground.
So yes, I have the capacity to help develop the concept at the level of reaction pathways, mass/energy balances, process architecture, catalyst choices, theoretical efficiency, refinery compatibility and economic modelling. We could even formulate it as a proper Artificial Resources research concept and calculate what a hypothetical 1,000-barrel/day artificial-oil plant would actually require.