Props on design, but very flawed logic. No basis for asserting that life or intelligence can't arise independently, and the "outside of natural law" quality of anything preceding the Big Bang removes it from the bounds of casuality. If the points you cited were all that was necessary to prove God, Hawking, who used theory to predict subsequently discovered phenomena like black holes, would have announced his "proof" of God. God's existence- either way- is unprovable, and a matter of faith.