If the universe turns out to be infinite, would we have to reject the Big Bang Theory? As per my understanding of the big bang theory, it stipulates that the entire universe was contained in this single point of "pure energy" and that the big bang happened when the universe rapidly expanded out. This, again as per my understanding, is derived from the observation that the universe seems to be expanding right now (Red-shift etc.) and so if we were to go back in time, the universe would be smaller and at some point back in the past, the universe would've been contained in one single point. 
However, my question is that if the universe turns out to be infinite then how can something infinite be smaller or contained in a single point? If you go back in time, the universe should be the same size as it is now (infinite) because it has always been infinite. An expanding universe would not be infinite but be finite, you would be able to traverse the entire diameter of it. A universe that expands out of something has a boundary, and so by definition should not be infinite. So, if the universe turns out to be infinite, will we have to look for an alternative to the big bang theory? I hope my question based on a meagre understanding of physics is clear.
 A: You question is answered in many different ways, but unfortunately they are spread  all over this website, but I would definitely read the link ACuriousMind provided in the comments,  Did the universe universe start at a point.
But, as you have put your own effort into thinking about the question, I feel I should give you my personal opinion (even though you didn't ask for it, sorry :), on how you might go about thinking about 1 specific aspect of your question. I say my opinion, because we have no evidence as to exactly how large the universe is or how exactly it started, (or even if it did start, at least in the way  we usually imagine the start of anything on Earth).
You might imagine the distance between objects on Earth has the same meaning as that of distance in space, say between the Earth and Mars. And it does, (as we have timed the signals from spaceprobes) and everything works out  but.........this definition of space purely as a distance could also be understood as  the relationship of objects to each other in spacetime.
To me, thinking of space in this way avoids a lot of the problems that thinking of space purely as a distance produces when we move to cosmological scales.   It is still a vague definition, but pushing it further is beyond my physics knowledge or else it's getting into philosophy.
A: The cosmological data is favoring either an open and likely or very close to flat or slightly positive curvature universe, possibly infinite,  and less likely a closed and finite universe. But it is within the margin of error, for open/closed/flat, and it is still theoretically possible that it could be infinite or finite and bounded (but very large). 
There are two types of geometries that describe the universe. The local geometry, and the global geometry. The local geometry is whether it has zero, positive or negative curvature. For the local geometry, if the spatial curvature constant is 0 or negative, the universe is flat or hyperbolic, and globally it can be infinite. If positive it is spheroidal, and finite. The measurements for spatial curvature are close to 0, but within the margin or error for any of the three. If it is a positive curvature the universe is still very large
In standard cosmology (with or without inflation, but standard cosmology includes inflation, or is thought of as evolution after inflation with unknowns before and then the Big Bang would not come in) the Big Bang happens at t=o, and although there could be all values of x, y and z present (if in doubt think of the Robertson Walker metric, with x, y and z just a system of coordinates in 3d space) it could be shrunk and have zero radius. The scale factor, a(t), is then 0. As it expands, i.e., $a(t)$ gets larger as t increases, the radius and spatial volume grows, or really evolves depending on $a(t)$
The above is all valid and physically and mathematically correct. The spacetime is a 4D manifold, with those 3D spatial volumes which can be stretched as the universe expands. And at one time (the Big Bang) it can have zero scale factor, but still has all of space coordinates there. 
Your more important question would then be, well, what about quantum gravity, which would be needed at the Big Bang? True, and the answer is we still don't know enough about quantum gravity to know. At those energies and sizes quantum gravity would be needed to describe it - maybe a string theory or some other quantum gravity theory that would explain what is the case then. Just like at Black Hole singularities, we just don't know yet.  
A: My answer to this is that form a physics point of view and not a philosophical point of view is that i think scientists currently believe that the universe was not created from a singular point but that it was created from an infinate number of points. ie the universe was created everywhere at a point in the past and has been expanding around those point since its creation. As far as picturing that scenario there' i think a statistist that has said theres a way of viewing infinity where there's degrees as to the size of infinity. Some are greater than others. But this idea that the universe is created everywhere has some evidence ie the cosmic background information perhaps read further there.
