The Russians did some research in the 1950s on the possibility that oil is not necessarily a "fossil", but is in fact capable of being produced by an abiotic process deep within the Earth in a continuous cycle, not unlike the recycling of crust at subduction and eruption zones around the world. I don't know a great deal about what they discovered, but I think they were closer to truth than anything in the current dogma about "fossil fuels".
And even if it is due to an entirely biotic process, most of that biomatter was not dead dinosaurs or anything like that. Most of it is marine algae, diatoms, and single-cell organisms. I'm pretty sure trillions of those things have been living and dying ever since, so is it not reasonable that the process that turns them into oil has likewise been occurring on a continuous basis?