Strictly speaking, the oil in the Earth's crust is both finite and more than 50% already extracted.

However, a closed cycle of renewable-powered vehicles and processing sites growing crops for biorefineries which are then hydrocracked into the various petrochemical additives to maintain the infrastructure with surplus left over for the rest of society has been proven to be viable going back to the early 2010s.

Leong et al has a great survey of how the entire market of irreplaceable petrochemical uses (e.g. medical grade plastic) and their upstream steps (e.g. metal smelting for making agricultural vehicles) can theoretically be made to work from wind alone, with total immunity to peak oil when it does eventually happen. Although the carbon molecules are essential, having a no-oil well industrial civilization is just a matter of long and arduous implementation and negotiation with vested interests.