For all practical purposes, I agree with the analogy, but would like to point out that the box might not be infinite so there could be limits to invention.

Take a chess game as an example. No one would say there weren't creative inventions regarding tactics and strategies to win, but the bottom line is that the number of possible chess games, no matter how staggeringly huge, is still finite. In the end, no matter how intelligent the players, there will be a point were nothing will be left to be invented, so perhaps life is also a solved game in that respect.