No, I'm not comparing the Sun to the BB. Why would you think that? I'm just talking about the concept of looking back in time.
The BB isn't the "center". The universe is the universe. It is all expanding , not expanding from a center outward.
There is no "half-way" point as you are describing. As was pointed out above in another post, there is the concept of the visible universe and what's beyond that. The visible universe is just the portion of the universe that light can get to from here in 14 billion years so it's twice 14 billion plus expansion. Any expansion beyond the speed of light will never be accessible from here.
My last paragraph is undoubtedly full of mistakes and is totally up for correction by anyone more knowledgeable on this subject.