Read Olbers' paradox first, or none of this will make much sense...
It would appear that having a "Big Bang" event would resolve Olbers' paradox: looking at stars further and further away means looking backwards in time, so after a certain distance no stars can be seen, and the paradox vanishes.
But models with a "Big Bang" are still of bounded (but with no boundary conditions) universes. And a bounded universe doesn't resolve Olbers' paradox. Adding the "Big Bang" event just means this bounded universe evolved to its present state (a bad way to pick up chicks (and, presumably, pick up studs) is to say at parties things like "Big Band cosmology throws away anistropy in the time dimension", so don't do that). So when we look further and further away, we're just wrapping around (á la PACMAN). The universe we're looking back at is smaller and smaller the further we get away, but eventually we'll still hit a star. In fact, we'll probably hit a star sooner rather than later.
So this (on its own) affords no solution to Olbers' paradox.