IIRC, the CE mark is self-prescribed, so a manufacturer may (in good faith) state that the product is compliant with the applicable European requirements, and that's that. 3rd party sign-off not required.
Only if the product fits in a category that doesn't require going through a notified body, such as medical devices. And a lot of others. So you need to check that first.
Now if your product can indeed be self-marked, it is true that the only required *paperwork*, strictly speaking, is the declaration of conformity that the company will write. Someone is going to sign it. Usually, it's either the quality director if you have one, or the CEO themselves. This is not just a piece of paper though. Signing it means you take full responsibility, and as Neilm said, you claim that your product complies with all applicable directives.
No one is going to force you to *prove* compliance at this point. Until something goes wrong in the field. If there's significant damage and someone sues the company, then one of the first things will be to check what the company did to ensure compliance. If the damage done is related, even remotely, to a suspected non-compliance to one point of a relevant directive/standard, and you happen not to have done enough to ensure compliance in the first place, and have not even tested it, then you're in trouble. The person(s) responsible (again CEO+quality director if any) may face penal charges.
Now the amount of work to do for any given product to reasonably ensure compliance is entirely up to you. It requires experience and knowledge, and a great chunk of compromise. And testing is not the only thing to ensure compliance. You need to have a minimal technical file describing the design of the product, part selection and manufacturing, and this cannot be done by an external lab.