How would you quantify an experience into a score without labeled data How would you approach a scenario where you have to quantify an abstract notion like “customer experience” without having any labeled data? So basically what you have are bunch of variables that you know, more or less, how they affect the experience, but you don't know the "weights" of importance of each one.

So e.g. if it is an experience from a food delivery service, then I have the ETAs for the order, ratings (not very reliable by the day), cancelation reasons, $ amounts, etc.
To continue with your example, a domain expert (or business expert) would have to determine which of these is more important and therefore should have higher weight.

They may care about ETAs for the order because their customers appreciate getting a fast delivery, but may not care as much about the cancellations due to a high amount of orders they have anyways. Now this is purely guessing.

In order to build a model that will suit the business's needs - this should ideally be discussed with someone who understands the domain well and knows what they want to achieve.