If we accept
1.that the notion of cause-and-effect is tied to time, and that
2. time is a part of our Universe only,
then we cannot accept an external creator. We can only see that time is a part of our Universe; there is no reason to believe that anything outside has to be time-based. We can only refer to causality inside our Universe (by premise 2.). So, what happened before the Universe was started? Well, there is no such thing as "before the Universe". Because there is no "before the universe", the universe cannot have had a cause, as cause is a temporal concept (by 1.).
Under this argument, it is in fact a category error to talk about the universe having a cause, as causal relations are only defined on temporal objects (which only exist inside the universe). It is like trying to perform addition not on numbers, but on sets of numbers.
If this argument holds,God cannot have created the universe, simply because cause is an undefined concept over things not inside the universe (Not even sets are inside themselves). On the other hand, if we accept that the universe and God are part of a temporal meta-universe, then God could indeed have created the universe. The compelling reasons for not doing so are that
a) We cannot detect this meta-universe, so to talk of it is purely metaphysical speculation.
b) We have not made anything simpler, as we can legitimately ask what created the meta-universe, if we consider questions about the origin of the universe to be legitimate.
Further, the above two points hold if we substitute "God" for meta-universe.
The weak point in this argument is the premise that causation is a temporal concept. This sort of thing vexes philosophers mightily. added 23/09/2002. For instance, as Tiefling says, "It could be conceived that the existence of the universe is a function of the existence of God". This does have the problem, however, that that we would have to find some way to detect God, beyond the fact that we (The universe) exist. There is also the issue of how we decide between the universe creating God, and God creating the universe. Then, we have to consider whether or not a God that is not separate from the universe is compatible with our favourite theology.