This is a major rewrite of my previous answer, so if you've read it before you might like to read it again. I'll begin with a definition: "to create" - Bring (something) into existence. (dictionary.reference.com/browse/create).
The question of what it means to exist is one that has been covered at depth by the existentialists. A pre-cursor to the existentialists, Martin Heidegger investigated that bit of reality which has the power to ask "what it means to exist", ie Human Beings. (Heidegger proposes this philosophical investigation in Being and Time, an outline of which can be found here.) The study undertaken by this route (continued by Sartre and the existentialists) seems primarily related to human existence, and not existence per se.
I hope that I can take another approach to begin to answer this question. I would like to propose that, based on the definition of "to create" given above, "to be created" should be defined as "to be brought into existence where previously one did not exist". If in fact to create is to bring into existence, before one is created one has not been brought into existence. Therefore an uncreated thing has either: always existed, or does not exist.
With some agreement on what it means to create and be created we can look at the thing in question, the universe. What exactly is the universe? There are many competing definitions available. For the purpose of this discussion I would like to appeal to scientific defintions.
Accepted scientific definitions of the universe have been and continue to be contested. At this point in time we can consider definitions from two camps within physics: the theory offered by Einstein's theory of general relativity and the theories offered by quantum mechanics. I'll consider each briefly.
"Relativity says space and time are on equal footing - together they are the fabric of reality" (New Scientist). The article this appears in goes on to describe that space and time are part of a single four dimensional fabric that can be modelled mathematically in ways that are very useful for predicting the behaviour of large objects. On this view, space cannot exist where there is not time, nor can time exist without space. Both include each other. If we say the universe consists of this fabric, I would argue that self-creation is not possible. The reason for that is that on this model the laws of physics hold. Effect follows cause. The effect of being created must follow its cause of creation.
Here we come to the nub of the question. Is it necessary to exist in order to create? Or more broadly is it necessary to exist in order to act or have an effect. I believe the answer to this is obvious, and so I will proceed without the support of refernces for this point. Let us say, at least for the sake of argument that to create presupposes to exist. Therefore the thing which creates the universe must exist in the instant prior to creation in order to create. While the universe, to be created, must not exist in the instant prior to creation in order that it may be created. This presents two opposing requirements that cannot be reconciled in the one thing, the creator must exist in the instant prior to creation while the created thing must not exist in the instant prior to creation. Therefore a creator cannot create itself. Thus the universe cannot create itself.
Yet the idea that the universe consists of a single four dimensional space-time fabric is contested on the minute scale of quantum mechanics. Space and time, may, when considered at that level, be separate, or they may both be expresions of a more primal reality (New Scientist as above). If the universe is defined to include this primal reality there may be scope for saying it created itself. However, to avoid an infinite regress you must say either that something always existed (and created other things) or that something came from nothing.
Depending on how much your "nothing" is actually nothing you may be more or less inclined to reject the notion that something comes from nothing, or that things can spontaneously occur without cause. If you do reject that, the evidence before your senses that there is in fact something, suggests that there always was something. The question then becomes what has always existed? Scientists mostly agree that the universe did not always exist (www.big-bang-theory.com). Theologians agree that God always does exist, on the basis of reason and scripture such as the following: "Before the mountains were born or you brought forth the earth and the world, from everlasting to everlasting you are God." (Psalm 90:2, English Standard Version).
