Believe it or not,
early researchers actually wanted to know why the universe was as uniform as it is. They couldn't
explain why the average temperature of the universe was the same in all directions, for example.
This was known as 'The Isotropy Problem'. This eventually led to the theory of inflation.
But your question does have merit.
There are several things to consider in answering this question:
#1) The Big Bang probably started with a tiny ball of pure energy that was much smaller than
a single atom. But it is important to note that at the instant of the "bang" there were no solid
particles of matter yet. Temperatures were much too high for solid matter to coalesce.
All that existed was spacetime and energy.
#2) Within the first 10^-33 second, inflation occured, in which the entire
universe expanded from less than the size of a single proton
to larger than a basketball. But this did not cause the type of
stereotypical explosion you are thinking of, but rather is was space itself that expanded
outward in all directions, carrying everything else with it.
#3) Even at its expanded size, there were still no particles in the universe yet due to the high
temperature. But what did exist right from the beginning was quantum uncertainty. The same
quantum uncertainty that is responsible for us not being able to determine the velocity and
position of a particle with precision, and also causes energy fluctuations in empty space which are
responsible for the continuous creation and destruction of virtual particles.
It is believed that quantum uncertainty is responsible for the non-uniform nature of the universe.
Random fluctuations in energy due to quantum uncertainty which occured right at the beginning
imprinted themselves onto this expanding baby proto-universe. And it was these patterns that
later served as the seeds for clumping once solid matter and gravity took over.
Over the next 14 billion years, the effects have become magnified many many times over.
But when you look at the night sky, you are really seeing the effects of quantum mechanics
writ large across the sky.