Well, the way they proved the number was 20 was by using a computer to go through solving every single case.
God's solution is basically the shortest solution, and that's not very obvious; remember that greedy algorithms exist, and though they appear to be making progress (e.g. matching blocks) it might not be the actual solution.
There is also the Thistlethwaite, Human Thistlethwaite, and Heise methods, if you are interested in solving based on fewest moves.
lol, here to help ^_~