You can run an industrialized economy on renewable energy. It just wouldn't look the same as the one we have developed in the presence of fossil fuels.
If there were a colony of modern humans established on an Earth-like planet that lacked surface coal seams, didn't have limestone deposits for cement, and lacked oil fields, you wouldn't expect them to shrug and say "Well, back to the stone age, I guess."
No, instead, they'd set up smart grid networks to use power when wind and solar were available and consume less energy when it was not. They'd use DC-DC converters that were more flexible under brownouts, where early energy systems didn't have that technology and had to rely on fixed transformers and fixed frequencies. They'd connect long distance, high-voltage lines between areas with hydro and geothermal energy to regions without, using pumped hydro storage when variable energy sources had excesses. Yes, they'd run Sabatier process factories to generate synthetic hydrocarbons for plastics and portable fuels, they'd precipitate calcium carbonate from ocean salts and atmospheric CO2 to make cements and ceramics; these would probably be less plentiful as a result of their cost and because they'd be aware that they don't decay but they wouldn't be nonexistent.
Our energy systems are moving bit by painful bit in this direction already. Indian, African, and other growing economies are growing in a world where renewables are cheap, where we have tech that makes them more usable, and where there's a lot of knowledge about climate and environmental science so they don't have to make the same mistakes we did.
Yes, the industrialized world works the way it does because of a history of fossil fuels. It may even have been impossible to jump-start the industrial revolution without them. But it doesn't have to remain that way.