Your argument is simply that the volume of the universe is infinite. The argument of a time before the big bang is simply that time is infinite. Logic doesn't require that the universe expand "into" anything, but if the universe does, than what do you suppose separates the universe from that thing? Inherent in your notion of that thing is that it is space. It is simply more of the universe.
The universe is, *by definition*, all that exists. There isn't an existence "outside" or "before" the universe. For the notion of a *finite* universe to have any unique meaning, that definition must be retained.
Maybe you are right and the universe is infinite. However, there is no inherent contradiction in the notion of an expanding universe of finite volume and time.
If the universe were infinite, it could not expand, as you noted. I do not hold that the universe is infinite.
The argument of a time before the big bang is simply that time is infinite
You are exactly right and I have to chuckle when cosmologists say, "Before the Big Bang there was no time." Time as we know it, linear time, is finite. I do not argue that there is not another kind of time outside the universe. God Himself is beyond the temporal and has demonstrated this in various ways including the recording of specific prophecies fulfilled hundreds or even thousands of years later.
than what do you suppose separates the universe from that thing?
This is a problem for which your cosmologists are attempting to create a theory. The question is "what happens when you leave space if indeed we can leave space?" But the answer to your question is, at this point, "space." Since the universe is expanding at nearly the speed of light, and since we do not have the technology to reach or exceed that speed, space is indeed the barrier.
The universe is, *by definition*, all that exists.
Yes, when we speak of the temporal reality in which we exist we can properly use that definition. But to say there is no other realm of existence because the universe is all that exists is to exhibit the fallacy of equivocation. The definition of universe cannot change in the same argument from:
1) This physical, temporal realm of existence
-to-
2) All realms of existence.
If you insist on the materialist presupposition that this is the only realm of existence, you remove your a priori supposition of the eternal existence of matter. Can you shape reality with only words? If I define "coffee cup" as something that can only hold coffee will it not still be able to hold tea or mercury or sand?