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Well yes, in due time, the acceleration of the expansion of the universe, will reach so high veloceties, that all residual evidence of big bang will be unobservable from any point in the universe.
Already today, it is estimated that we can only observe about 5% of the universe. Luckily that includes background radiation and far away galaxies moving away from us. So at least we know there was a big bang, and a huge number of galaxies. Future civilizations (think in the order of tens of billions of years from now) won't be that lucky. to them, the universe will look as it contains just the galaxies in their local group. Everything else, just a big black void.
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