I was watching a documentary and they said that Cosmologists have determined that the Universe is infinite. I find this to contradict the expansion theory. If the Universe had a starting point then how could it be infinite ? It can only reach out as far as it has expanded in the age of the Universe, 13.8 billion years . If it was infinite then it would not be expanding because it would already reach out to infinity. I hope it is clear what it is that I am trying to say ?
There are infinite number of points between 0cm and 1cm on your ruler, there are also an infinite number of points between 0cm and 2cm but it is plain that the 2cm gap is twice as big.
This is not an exact parallel (or even a very good inexact one) but is offered to show you that infinity may mean quite a lot of things: for instance what if space were infinite before the big bang but what happened then was that "things" (ie the spacetime metric) became ever further distant from one another - if space was already infinite then this expanded space could not reach a limit.
In geometry one may have a line segment, of finite length, with defined start and end points. One may also have a line, continuing without bound in both directions. Then again you may have a ray, which has one end, continuing without bound in one direction. You could even have a circle, with no end, but finite length.
Now what is the time dimension of the universe like? That depends on how space-time is curved by the gravity of the mass and energy in the universe. Measurements suggest that time in the universe has one end, at the "big bang", but continues without bound: an "infinite universe"
Without knowing the exact context it is hard to be certain, but my guess is this is what is intended. The universe has start time, but no end time.
I think you're operating under a few false presumptions, the first being that that all infinities are instantaneous, which they are not!
Imagine I told you to start counting at 1:00 PM tomorrow, starting at the number one, and then to keep counting, once a second, until I say stop.
So at 1:00 PM you'd start: 1...2...3...4...
At 1:05 PM you'd be at: 300...301...302...
And at 1:10 PM you'd be at: 600...601..602...
Ok now I tell you to keep counting to infinity, so that you never stop counting! Eventually you'll reach every number you can think of (and even more, since you can always count another second after the one you just got to), but it might take you weeks, or months, or centuries to get to there!
So in that example we had a start, 1, and we're going all the way to infinity (i.e. we'll never stop). In the same way, the universe could start at one time and keep expanding forever (the only difference is that the universe "starts counting" at 0 instead of 1).
But why 0 and not 1? Or 2? Or -356? Or even -infinity? Why did the universe start 13.8 billion years ago? What about the time before the big bang?
This is a very, very tricky question (and one which may never be answered), but most cosmologists will tell you that there was no time before the Big Bang (since there was no space!), and even if there was, we probably wouldn't be able to probe it.
I will suggest you check out Sean Carroll's blog with a few great explanations to these kind of questions: