Christian theology has always taught that God creates ex nihilo, from nothing. God's relationship to the universe isn't analogous to the one that holds between an engineer and his machine. The engineer merely arranges preexisting component parts in such a way as to make them serve a beneficial purpose. The parts themselves don't depend on his activity. The God of traditional theism, in contrast, gives every thing its being, not just its structure. Rearranging preexisting bits of matter doesn't strictly bring about new being, rather it changes the being that is already there. Hence, God's job description requires him to create ex nihilo.
This might seem odd, or even unintelligible at first : how can anything be brought into existence from nothing? When we create things, don't we always do so by putting bits of matter together?
But as strange as it is, creation ex nihilo is all around us, even though (and as we're about to see) our linguistic practises tend to obfuscate this. Take, for instance, the case of an object heating up due to being left out in the sun. The standard explanation of this, which we all learned at school, is that something is being transferred from the sun to the object. That 'something' is thermal energy, or simply heat. Our 8th grade science teachers would have us believe, then, that heat is a 'thing' that can passed on from one object to another, like a baton.
The problem with saying this is that heat, unlike a baton, isn't actually a thing! Rather, it is a way a thing is, just like colour, weight or shape. It doesn't have its own existence, it cannot logically exist without being had by anything (no such thing as heat without some hot thing). Therefore, unlike a baton, it isn't something that can literally be passed on from one object to another. When we say that heat is 'transferred' from the sun to the object lying outside, we mean to say that the object acquired a new way of being, namely being hot, as a result of the sun's acting on the object. Crucially, this new way of being isn't some preexisting part that was attached to or incorporated into the object -- parts can conceivably exist without the things that have them, ways of being cannot. Hence, the object's new way of being did not preexist the object. It was given to it from nothing.
The same lesson applies to all instances of so-called 'energy transfer'. In all such instances, an energy source brings about new ways of being in other objects, without literally giving them some preexisting thing. If this can be done by a burning ball of gas, surely it can also be done by God. The difference is merely one of degree: the sun gives the object some of its being ex nihilo, i.e. its heat. God, in contrast, gives things all of their being.
But there is more to the analogy. While the sun creates in the object its heat ex nihilo, this does not mean that the sun is radically unconstrained in what it can bring about. Specifically, it can give no more than what it already has. It is able to make the object turn hot, only because it itself is hot. We may say that the object acquires its particular way of being by 'reflecting' or 'imitating' the sun's particular way of being. There is therefore a sense in which the sun shares some of its own being with the object. Again, the same applies to other energy-sources.
If this is the way in which new ways of being are brought about within the natural order, there is no reason why God shouldn't bring about being in this manner as well. There is therefore a sense in which divine creation is ex deo, i.e. 'out of God'. God creates by sharing his being with the rest of reality, which reflects his being, each particular thing in its own way.
We may draw two conclusions from this: first, that divine creation itself is a self-giving act on the part of God, who 'radiates' his very self to creation. Secondly, all created beings, as Leibniz put it, express God to various extents, depending on how much of himself God shares with them.
"For with you is the fountain of life, in your light do we see light" Psalm 36:9