There are alternatives to fossil fuels. You can make hydrocarbons from many sources and use those to make petrochemicals and additives.
There might be some argument to be made at how inefficient such processes would be, but they would still be viable.
Solar powered mining equipment to extract raw materials, solar powered arc smelters for refine materials, solar powered CO2 extractors to create simple hydrocarbons, engineered bacteria for more complex hydrocarbons. Which you will need for a lot of chemical reactions to make modern technology. Just need a lot more square area to do the job. Basically instead of using minimal energy to extract and then burn energy that was stored a long time ago by plants.
There is also some concern in absorbing too much solar energy rather then letting it bounce back out. But there are solutions to that if we really had to. Such as large orbital sun shades.