Believing in God takes you into the Spiritual side of the concept which is Faith and I will discuss that in my discussion of Faith. Believing, when it comes to spiritual matters, is often a matter of both evidence and experience; it may be based on personal experience--such as feeling the presence or power of God acting in your life. Often such things take a leap of Faith to feel the experience, but sometimes the experience disrupts our doubt, grabbing attention. Is anything truly unexplainable? The miracle of life has scientific explanation. The stars in the heavens are giant balls of gas many light-years away. We are all made up of chemical compounds reducible to the components within atoms. Some might therefore say that everything has a rational explanation and we simply have not discovered all of them.
To me intuition is a part of our Higher Power and that power is what I refer to as God. A mother's intuition spikes when caring for her newborn and hormones may be part of the explanation. But is that sort of explanation sufficient to explain how she may know her baby is in imminent danger when the distance between them is significant? It's not for me. And if such a thing is possible between a mother and her infant, it could be possible between other relationships too--why not? Could it not be possible that intuition is a skill that can be enhanced--and yes, some may come to it more naturally. Who or what gives these intuitive messages or signals? The messages transmit through various methods, voices, somatic feelings, visions, dreams... Yes, there is a gap that crosses from believing where there is more concrete evidence to faith where the evidence may not be understood or have an explanation we are ready to accept.
Believe in the possibility of such things for you. That can be difficult when you lack personal experience. But consider why? Doubt? Perhaps, but there are other explanations. Many believe and yet the experience eludes them. Emotions that hold a person captive such as rage, fear, stress, anxiety and panic all block energy which communicates intuitive messages. That is another reason Self-focus is so important. It opens you up to communication with God. Sure, He may be communicating with you regardless, but are you receptive? You can choose what you believe.