Are the Big Bang and Genesis mutually incompatible?

Depending on how literal you take Genesis, they are mutually exclusive. However, if you are willing to acknowledge that the Bible is primarily made up of parables, you can have a creation story that acknowledges the existence of a god while also accepting the theory of the Big Bang.

Rather than claiming there is no god, Stephen Hawking has said he does not need a god to explain how the universe came into being. He does not deny the existence of god, but he also does not attempt to disprove it.

In general, there is no reason to believe that the Big Bang theory and the Genesis creation story are incompatible. A number of religious interpretations, including some that are found in Christianity, see the Big Bang as consistent with the idea that God created the universe, and they see it as the scientific explanation for how God initiated the universe's existence. On the other hand, some interpretations of Genesis may be at odds with specific scientific details of the Big Bang theory, such as the timeline of events or the mechanism of creation.