Is it possible to make synthetic oil without fossil fuel?
Yes, it is being theorized and it's being done: 

Example A:
https://www.researchgate.net/publication/264810861_Engineering_cyanobacteria_for_production_of_a_cyclic_hydrocarbon_from_CO2_and_H2O

Example B:
https://www.sciencedirect.com/science/article/pii/S2211926416304982

Example B is more theoretical with economic considerations, and example A is more methodical. In these papers, we see cyanobacteria being used to make the aromatic hydrocarbon limonene with the limonene synthase gene derived from a plant. 

As for can we make synthetic oil that is chemically proportional to fossil fuel, Probably not ... but by adjusting the ratios of aromatic hydrocarbons, we can measure some useful properties like the heat value of the fuel for which limonene has a heat value very close diesel fuel and the density is close as well as you can see if you read the aforementioned Life Cycle Analysis paper. If you want to explore the chemical composition of fossil fuel then you need to do some spectroscopy work.

But fossil fuel isn't perfect. There is residual incombustible material, and perhaps by adjusting the proportion of combustible aromatic hydrocarbons in fossil fuel maybe we can get more energy from fossil fuel. This is also a function of the funding that these research projects get and also industrial support which is also a function of money ... which is why you need high yield in these reactions, hence genetically engineered cyanobacteria.