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There are a couple of big leaps of the imagination you need to take
The first one is in the nature of space and the second is in the nature of time
So nothing much really! :c)
A good question is how we know that it is space that is expanding an not a gigantic lump of matter exploding into existing space
The answer to that goes back to Hubble and his law
Hubble discovered that the further away an object is the faster it is receding from us
That's very different from an explosion - in say a handgrenade exposion you would expect all the energy to be transferred at the explosion and all the shrapnel is flying apart at roughly the same speed.
What is happening in space is that it's expanding - every little bit of it. the further two objects are away the more space is between it and so the larger the effect.
Run that backwards and what you get to is a very small point
One of the problems is in dimensions we are aware of 3 but there may be more - we can't imagine them any more than a goldfish imagines outside of the water - this book would blow your mind :c)
http://books.google.co.uk/books/about/Flatland.html?id=h7AN6hI5Ze0C&redir_esc=y
As for time - well that really doesn't work the way you think it does, it goes faster or slower depending on all sorts of things.
An important way it goes slower is in the presence of large gravitational fields - time goes quicker for satellites and your GPS wouldn't work without adjusting for that.
Now think of this when we say the Universe started x billion years ago what do we mean?
Well if you track that big bang back that's where you get to assuming time tracks the way it does now for you and I at our keyboards.
Now imagine we spin the clocks back while we ride the Universe back
As it gets smaller and denser time slows denser and denser slower and slower and we never get to zero
So in a sense if you're 'inside' the Universe it is infinitely old - it has always been here
Whether the Universe started as a big bang or whether it has always been here depends on where you're sitting!