Are the Big Bang and Genesis mutually incompatible?
It depends how literal you want to be about Genesis. If you are absolutely literal then they are mutually exclusive. If you are willing to accept that the Bible is mostly parables, then you can have a version of creation that includes a god but also agrees with the Big Bang.
Stephen Hawking actually has stated he does not need a god to explain the creation of the Universe, which is a lot different than saying that there is no god. He doesn't believe in god, but he doesn't try to prove there isn't one.