I would think that everything would be moving in relation to everything else.
The original light of the "Big Bang" event is long gone absorbed by objects transfered into heat.

Perhaps if you had already existed in a different universe you might have seen the events light as being blue shifted Ie coming at you but it would be hard to get it coming at you if you are a part of the event.

However there still may be hope!
With the recent discovery that light can be stopped in a super cold condensate perhaps such a substance exists somewhere in our Universe which trapped light from that event and it is just waiting to be found and analyzed.

The common conception of the "Big Bang" event, I believe, is that the Universe was formed by a massive explosion with a nice sphereical shape and all pre universe matter was used.
My postulation is this: What if the Universe is only an eruption like a solar flare and most of the matter wasn't used?