Why would it be bright white?
Inadequate explanation. Even if the universe was a closed box with perfectly reflecting borders, what you would actually see in the sky is something like an average brightness of the entire universe with some fluctuations.
Light scatters, gets absorbed and re-emitted, it's true, but if distances don't change then the universe would still be much brighter than it is today.
Only if you think that there is infinite matter, all of it forming the same kind of stars, uniformly spread over the infinite space and there is no unknown form of atenuation for waves traveling millions or billions of years light.