How is your first time spoiled by waiting until your next day off work? The game will be there and you can have you first time for all those things whenever you get to it.I disagree with the "it'll always be there," because it's like a movie. Yeah, you can watch it again, but you never get a first boot up sequence ever again, the feeling of stepping into a world for the first time and trying to understand how it works. The big reveal of the twist and that first walkthrough where you're more interested in getting there than the desired destination. The first time I booted up Skyrim I didn't know what the fuck I was doing and just wandered until I ran into something to kill or, in most cases, something killed me. In Fallout 4, my first character was the mother just trying to find her kid and following every path that pointed in that direction (and eventually joining the Institute after finding out your son had grown into the leader of the Institute). You don't get that first time ever again.
I don't see how your story has anything to do with having to absolutely experience it ASAP. People don't see movies on opening day, often waiting for the weekend (when they're off work) to see it and their experiences are just as good as the people who stood in line at midnight release to watch it. Arguable their experience is better because they wont be trying to play/watch it tired.