Opening the book…
A metric is always a proxy, and the gap between the proxy and the real goal is where all the later damage lives. If the goal was never stated, nobody can see the gap widening, and arguments about the metric turn into arguments about nothing. Writing the outcome first also exposes the cases where you don't agree internally on what you want — far cheaper to discover now than after a dashboard has been built on the disagreement.
Write one or two sentences, in ordinary words, naming who is better off and how, with no metric nouns in it: "customers get their issue resolved on the first contact and don't have to chase us." Get the people who will be judged by the measure to agree the sentence describes something worth doing. Then keep the sentence attached to the metric everywhere it appears — in the spec, the dashboard, the review deck — so the proxy can always be read against it.
Exploratory measurement, where you are watching a number to learn what is happening rather than to steer anyone, doesn't need a stated outcome yet; it needs one before you attach any decision to it.