I think one improvement would be to start with a very obvious puzzle in the first letter. The day 2 puzzle is, in my opinion, the most opaque: when reading that letter I did understand that there was presumably a puzzle (thanks to the narrator hinting as much, and the fact that the envelope labels were so unusual) but I couldn’t get anywhere with the puzzle so I assumed I had missed something earlier, or had to wait to solve them in a second playthrough, etc.