...argues that the Universe's order is evidence of God's existence. This is a common argument, but as many have repeatedly noted over the years, orderliness cannot logically be evidence of a "first cause". For if God created an orderly universe, it must be because some part of God is orderly. And if the fact that something is ordered is evidence that it was created or designed, then God himself must have been created or designed. Thus, if we accept the "argument from order", we must conclude that God was created, as was his creator, and its creator, etc.
The "argument from order" simply kicks the can down the road. As with most logical proofs of God's existence, it results in an endless regression that ultimately explains nothing.
That's not to say that there is no God, only that he/she/it can't be proven through logic.