They are not mutually exclusive. Let's consider first the case for believing in God. And let's use miracles as our starting point. Christian faith believes that the Bible is full of miracles. These miracles, we believe, don't prove, but do point to the existence of God.
Many scientists say there is no such thing as miracles, that is, supernatural intervention.
Everything can be explained through natural processes, they say. Therefore, there is no God. I believe you can believe in God AND science. Because science has its proper field of study, and faith has its field of study. Let me show you what I mean.