Contrary to
popular belief, modern
cosmology doesn't give the
Big Bang a specific
location. Instead, the
Universe expanded from a
zero size (if you believe in
Relativity) or from a size dependent on
Planck's constant (if you believe in
Quantum Mechanics). The precise analogy is that of a
balloon inflating, but imagine it starting from zero size. So all
points originate at that
singularity, and the
Big Bang can be said to have happened at all points.
In particular, you get uniform background radiation of 3°K.