Is light explained by the Big Bang? If so, how?

Your question is so vague as to be hard to answer.The existence of light is explained by the big bang theory, or more accurately by the star formation theories that chronological follow the big bang.The nature of light is not explained by any current scientific theory; although String Theory looks like it might be capable of doing so.

I think quantum electrodynamics (QED) "explains" light very well. Now I would need to know what you mean by "explain". Light isn't a major mystery unless you want to keep opening up the next box down and have to explain exactly why the universe is as it is. That is where string theory might come in.

While we can predict the behaviour of light very well, we don't know why the constants controlling that behaviour are as they are. They appear as 'magic numbers' in Quantum Theory.

The problem is, no one actually knows what the intital conditions of the universe were. If we assume an empty universe in the beginning, inflation may be the explanation you're looking for. If you're wondering how EM and spacetime itself are fundementally related, you'll have to wait for a quantum theory of spacetime.

Of course, I agree with that. Which is what I thought I said at the end of my post.

K, got what I was looking for.