The Big Bang and the original size of Universe

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If the Universe occurred and expanded (plum pudding model say) how much 'space' did it occupy at the outset?
I am trying to understand / visualise, recognising that the Big Bang is not thought of as an explosion, how the Universe could have come into existence as a 'point' but came into existence 'everywhere'?
Is it a concept that such a point was then everywhere, and that the mass of the Universe, as is now, was coalesced into that point?
I am just in my first year of the physics degree and my maths does not extend to any great degree, but is it the case that the maths quantifies an opening situation?
Martyn
 

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