If space has a limit, then all space would be finite.
Until we agree on what is considered "space" this argument is pointless and i am not going into a stupid "frame of reference" style argument. So, let us agree that the other will never agree, and move on.
Nothing to do with for's. Two definitions of 'universe' exist. The traditional one, means the limitless space, all and everything. The modern one meaning the space our big bang system is limited to. For some reason the modern version has become the popular definition based on a theory that cannot be proven. The problem comes when pseudo-intellectuals use one definition while talking about the other. The big bang theory is just that, a theory. Many scientists consider it Hawking fiction, and no more than fun reading. It is so full of holes, and dependant on so many unknowns, yet we use it as a foundation for our terminology and referencings. It's absolutely silly.
I agree about finite space only being able to hold a finite amount matter. But wait, why do you think that? If the entire universe can be contained within a volume of no dimension, a singularity, how do reconcile that you think infinite mass is possible and yet not? Which is it?
And you avoided so many of my questions about the nature of the big bang. The most relevant being, how does an infinitely dense object explode in response to itself being too dense? Meaning, at which infinity does infinite mass become too massy?
The scientific community has made the mistake of blind acceptance before. And not just in the distant past. In fact, even with Hawking. When Hawking asserted that information is lost in a black hole, the paradox was readily accepted by the majority of the scientific body. This was true for decades. Subsciences, like string theory, were based on it. Today we have the same problem with the big bang. Why are you so blindly accepting this notion? What happens when we disprove the theory, as Hawking disproved his own paradox? Will you continue to hold to the big bang? Will you continue to make your assumptions and false phrasings? Seriously, the universe has always meant the entirety of space, without any bounds imposed by highly theoretical conjecture.