Should I unbox and set up the P1 before wrapping it for my son's birthday?

Let him do it himself. I set up an A1 mini for my daughter last year and made the mistake of doing the whole thing first so it'd be 'ready' for her. She poked at it once, printed the little boat that was alredy on the card, and never touched it again untill she saw videos of people printing thier own designs. The unboxing and setup IS the fun part for a kid that age. The good news is these machines do almost all the calibration themselves, so there's very little he can get wrong on day one. It walks you thru the app, does its own checks, and the first print is basically ready to go. This is not a bed-leveling-with-a-piece-of-paper situation like the older budget printers.

On the filament question, the machine ships with a small spool in the box, so there will be something to load on day one, though it runs out fast if he gets hooked and prints nothing but benchies for a week. I'd grab a couple of extra rolls anyway. My other suggestion is to be physically present but useless on purpose. When my nephew got his I hung around reading the quick start guide over his shoulder and only answered questions when asked, which somehow made the whole thing feel like his project instead of a hand me down. Teenagers are weirdly good with the app side of these things, honestly better than I am.

One thing I'd add on the filament front, that sample spool that comes in the box is usally a pretty dull color. I've put about 400 hours on my P1S since spring and every early print I made in that free gray looks like a paperweight now. If you want the first week to feel exciting, order a roll in a color he actually likes so it's sitting next to the printer when he opens it.