If you agree, as do even Hawking, Einstein, Jastrow and a host of other renowned scientists and philosophers that either the universe had to be self existent and eternal (which I do not believe because it has been shown with overwhelming evidence that our universe had a beginning) or the Cause had to be self existent, without cause and therefore eternal, outside of space and time, therefore out of the reach of science. Perhaps a crude analogy would be that of an archaeologist who finds an earthen pot with handle, spout and engravings in an ancient unknown language, and although he can't prove who the potter was, he rightly concludes there was a potter of some intelligence behind the pot.I think we can both agree (along with the majority of scientists) that our universe is expanding, and that it "began" at some minute point. I can see how you're drawing your conclusion of an eternal creator: because time is a part of our known realm of physics, and because our laws of physics breaks down at the singularity, anything outside of that known realm of physics is not constrained by those rules; therefore whatever caused the big bang does not conform to the laws of time, and is therefore "eternal".
Here's where I think that argument falls apart. You are using the word "eternal" when the word itself implies time. Before big bang theory, it was believed by scientists that the universe was eternal, because we had no concept of the fact that time could not exist. That belief has fallen by the wayside as more have come to accept the big bang theory. If you accept the big bang theory, you must also accept that without the universe, there is no time. You can go so far to say that the universe has existed at every point in time, and that at no point in time has there been no universe. That's about as close to "eternal" as we're ever going to get.
When you really think about it, in the way that the word "beginning" is normally used, it's difficult to conceive how the universe can be said to have a beginning. When you say that something has a beginning, that generally assumes that there was a time before that beginning. The problem with your argument is that there was no time before the universe. Without time, the traditional idea of "cause" no longer applies. It's impossible for our minds to grasp a concept of anything without time -- we can only represent such an idea mathematically (such as in string theory).
As I said in my last email, any ideas about what happened before the big bang are pure speculation. This means that because we have no idea of what a world is like that does not conform to our known laws of physics, we cannot draw any conclusions about such a realm -- whether that conclusion be an intelligent creator or M-theory or whatever. Until the known laws of physics (which are changing year-to-year) can be expanded to cover such a realm, any premises based on it are meaningless.