As we look at other galaxies we are essentially looking back in time. Can we look back far enough to see the big bang itself? If this is so and c is constant, how did we get here before the light arrived?
It turns out that we cannot see the Big Bang for a "technical" reason. If you think about it, we can use light to look at distant objects because light propagates freely from the matter which emitted it. This was not always the case: when the Universe was less than 100 000 years old, the matter and radiation were so densely packed that light was "coupled" to the matter. This means that light which was emitted when the Universe was less than 100 000 years old couldn't "go anywhere", and hence can't reach us today. Observationally, this means that when we try to look at higher and higher redshifts, we hit a "wall" corresponding to the redshift when the Universe was 100 000 years old. This wall is the cosmic microwave background, or CMB. Look at this topic page for more information for more information about the CMB.
So, we cannot look back to see the Big Bang. And, since the expansion of the Universe has been less than the speed of light since the emission of the CMB, we do not have to worry about the problems you mention.
This page was last updated June 27, 2015.