Evolutionary Atheists: Irreducible Existence, your thoughts?

The theory of Irreducible Existence describes the inability to reduce the existence of our universe from the current state of existence to any former state of non-existence, thereby creating the need for an eternal original source for our universe. The theory states that everything that exists must be traceable back to an original source, and that this original source must possess certain attributes, most notably of which is perpetuality. The logic of the theory is that if something cannot bring about its own self out of nothing, and if something now exists, then something always existed. Some creationist proponents have used this theory to argue that our our original source points to the existence of God through non-transferable attributable association, which is the argument that God must exist if any non-transferable characteristic of him exists. In this case, they argue that eternal existence is one of the non-transferable definitions of God (meaning anything that is eternal is God, or is part of God), and therefore if our original source is eternal, then our original source is God. Your thoughts on this?