Adding to the ultra necro post here to confirm a few details. My first time running the first mission, as soon as I led Leon to the exit, the crate popped up on my mini map. I flew back to it and tried to click it, but the message I got said, "You Can't Complete This Objective Yet." So, you really can't get the handwritten note on the first playthrough, even if your first playthrough is via flashback.