There's a company that sells a version of the Finnish baby box, and we got one for our kid: http://www.babyboxco.com/ - everyone loved it. My wife is part Finnish, but we're in the US, so this was a good approximation.
I have a question. Our first child is due this week, and we also got a box from babyboxco. What did/do you use as sheets for the box's pad? We noticed this week that the sheet that came with it is just a non-fitted one that fits a regular-sized crib.
Congrats! I think we used a pack-and-play sheet, which was too big and we just rolled the edges under.