On launch day the visitor arrives from a tweet, a newsletter, a community post, or a friend's message. They know roughly nothing about the product, they are mildly curious, and they are comparing you to the ten other things they opened in tabs that morning. Two weeks later a visitor arrives from a search query or an ad. They have a problem, they are looking for a solution, and they have never heard of your launch. Writing one page for both is how teams end up with a hero that says "We're live!" to someone who does not know what "we" is.
The launch-day page leans on the moment: who built it, why now, what early adopters get that later buyers will not. The evergreen page leans on the problem: what the visitor is trying to do, how the product does it, and why it beats the thing they are using today. The practical move is to write the evergreen page first, because it forces you to state the promise without the crutch of excitement, and then adapt it into the launch version rather than the other way round.
If you only have time for one, build the evergreen page and add a launch strip to the top of it. A page that can sell to a stranger with a problem will also sell to a curious early adopter; the reverse is not true.
Before you point launch traffic at the page, a landing page audit shows whether the promise, the proof and the next step survive a cold read.