If time exists in the universe, but not the universe in time, the universe does not have a beginning in time, rather time has a beginning in the universe. The universe (i.e. "existence") may be uncreated and have a timeless aspect.
I agree with you that the creation of the universe was the beginning of time. However, if the universe had a beginning, it cannot be eternal or uncreated.
Anyway, much of the force of the question "why is there something rather than nothing" is actually incredulity at the idea that anything can exist at all without some explanation of how it got there (why not "nothing" instead of God?), and in this sense the incredulity applies to eternal beings (such as God) as much as anything else.
I disagree. An infinite series cannot be an explanation for something's existence; that is no answer at all. Keeping in mind that the universe had a beginning, we know that something had to make it. Nothing has to cause a necessary being (God). He necessarily exists. So the argument does not apply to God that He needs a cause. By definition, God is that which none is higher in being. He is perfect. If something created God than the God which was created is not God.
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