I don't think you'll like the answer.

There's a couple of parts to it, and I'm not an expert--someone who deals with "theories of everything" could probably tell you more, but I don't think there's someone like that on this forum.

The first part is that you're basically asking for the answer to "how does a universe come to be?" The problem with that is that there are very few ways to approach that question--all our scientific measurements take place within the universe and all our models deal with measurements within the universe. One hope is that if we can come up with a theory that describes everything in the universe in simple terms (string theory being one candidate) that it would tell us about the allowed structure of the universe or universes and perhaps how they came to be. String theory does indeed do this to an extent--predicting that an infinite number of universes exist all with different parameters. (I don't know what it says about finite vs. infinite universes, but if I had to guess, it would allow both.) Is this useful? Is this even science? I'm doubtful. It may explain our universe very well, but can we ever test its predictions about other universes?

The second part is to ask yourself why you prefer a finite universe or why you feel an infinite universe is impossible and check if there's a scientific reason to think so. The usual reason is that nothing we can measure of starts off infinite, so why should the universe? And everything that we know of that starts off finite and grows does so at a finite rate, and so can never become infinite in any of our measurements. That's a logical reason to say that nothing can be infinite, including the universe. That would also be an erroneous conclusion. Why? Everything we measure is within the universe. In fact, everything we measure is within the observable universe, which is certainly smaller than the entire universe. So we can apply this logic only to the class of objects "things within the (observable) universe." Since that class does not include the universe itself, it's flawed reasoning to try to apply these limitations to the whole universe. This doesn't help us come up with a plausible reason why the universe could be infinite, but it demonstrates that there's no plausible reason why it couldn't be and that the usual arguments are flawed.

So what is a model that might work? One that I've heard of and that makes some sense to me is that all possible universes at all possible times exist as a set of states. We say there is time and space because our brains and bodies work in a certain way to put ordering to these states. We process information by moving "forward" in time (converting energy to entropy) so we see an arrow of time. Various parameters of our particular universe define what we can interact with as we move in time, so we experience causality, etc.

So what might we see if we could step outside our human brains and look at the set of states making up our "universe"? It might just be that each universe is completely generated from a small set of parameters. From those parameters, you can imagine generating an entire set of states of the universe, which when placed in order by things living within the universe, form the entire universe from start to finish. From the outside however, you'd just have a list of parameter values for each potential universe from which you can generate an infinite set of states. Some of these values might make observers within the universe measure it as infinite and some might make them measure it as finite.

One last comment: theories of everything are pretty far out there and I take them with a huge grain of salt--I view most of them as philosophy with a lot of math rather than physics, since they don't make testable predictions. They also veer alarmingly close to what we see in New Theories where promoters of crackpot ideas will say "you have to free your mind for a paradigm shift" or somesuch nonsense. But the important difference is that while you do have to be willing to consider "really out there ideas" when thinking about the origin of the universe, all ideas are going to be about as far out there, since they all deal with the creation of the universe, which is something we don't have a good way of scientifically probing. As I mentioned at the start, you have just as much scientific evidence and justification to back up your "common sense" ideas as you do to back up the idea that the universe started off infinite or even that there's an infinite number of universes, some of which are finite and some of which are infinite.