Not a swatch guru, but I do have the MoonSwatch Mission to the Sun
I looked at the purchase receipt, all over the exterior of the box, miscellaneous papers that came in the box at the time of purchase, and on the back of the watch itself. The only number that stood out was on this stamped card (circled in red). Though, I doubt that’s a serial number.
Edit- as I suspected, that number circled in red is just the reference number to the Mission to the Sun.