Paul Hollister wrote:
Although the Big Bang Theory is mathematically sound, the a priori existence
of a nearly infinite supermassive density from which the big bang arose is
an unsupported assumption...

May I suggest reading Alan Guth's book.
http://scienceworld.wolfram.com/physics/Inflation.html

Also you might want to look at Ned Wright's Cosmology Tutorial:
http://www.astro.ucla.edu/~wright/cosmolog.htm