Does "Big Bang" Theory Invalidate Epicuran "Eternal Universe" Theory?

No.

1. Even if there was a "big bang" in our part of the universe, and indeed that would seem likely under Epicurean physics, what Epicurus was talking about as eternal is the "universe as a whole" - not any part of it.

2. There are scientists on both sides of the question of whether the universe originated in a big bang. For scientists who reject a "universal big bang" approach, including "tired light" explanations of contrary arguments, see references here.