In the US, I understand that the NRTL must evaluate and test the product and after approval, must conduct quarterly safety inspections. How can an EU consumer know that products are safe when manufacturers do their own conformity assessment?

EU authorities believe that competitors police each other. If a company or consumer thinks a product is unsafe, they can ask the authorities to investigate and test a product; if found unsafe, the manufacturer/importer is required to correct the problems or take the product off the market.