Dawkins criticism of Aquinas' cosmological argument fails because he does not understand the argument, and the distinction between causality in fieri and causality in esse. This distinction is taught in any basic philosophy of religion class, but Dawkins is ignorant of it. That does not mean the argument ultimately succeeds, but it does establish that Dawkins does nothing to refute it. Dawkins sets up a straw man and succeeds in knocking it down.
Further, Dawkins needs to come to grips with the Kalam Cosmological Argument. This argument does not only argue more successfully for God than does Aquinas, it also gives reasons to consider the cause of the universe as having the attributes of God.
