Based on the Big Bang, the universe is finite.
That isn't how it works. The Big Bang occurred everywhere in the universe, when all matter was condensed into a singularity and began expanding suddenly and quickly. It is conceivable that some area of the universe may be largely without matter in it (we've found such an area), but, as far as we can tell, the universe is infinite and expanding.
It is really hard to explain adequately and in a comprehensible way.
I think I get what you're saying, but let me add this: The big bang was the expansion of that singularity, yes. Everything from that singularity IS the universe; there is a 'limit' to the universe; the edge of that expansion. What lies BEYOND that expansion is not the universe. It's just nothing. No dark energy, no dark matter, no matter, just....nothing. A true void, a true 'space'. No atoms. No molecules. None of the fundamental forces, no rays or spectrums, nothing. Unless another universe exists in that void as well, or on a whole other 'plane' entirely, on another leaf/side of paper, if you will.
If you could get beyond the universe into that void, you could turn around and possibly see the universe in some form; though it does beg the question since it's outside the universe, would you, if you could get there, even manifest in some form? Would the laws of gravity, attraction, and matter and everything else work there? Or would one begin to scatter as the laws of the universe, also held by the boundary of the expanding universe, decay at the edge or right after it?
Since faster than light travel is impossible on the laws of physics we have now; and even if it were it would be a
logistical nightmare to reach the edge of the universe, those answers may very well go forever unquestioned. But they can still be at the least asked, eh?