If God has reached across the chasm of knowledge that divides us from the ultimate reality, then we must have some means of knowing him.Some people believe that we can encounter the divine through religious experience, whereas others believe it is though faith, though the two are not distinct processes.
There are different opinions and understandings of faith, far too many to go into here. But I believe that faith is a sense that one has been touched by something higher, that a higher being has encountered you in some way.
Here is where we reach a crossroads, for there are assumptions about experience that define your starting point for your rational quest. Do you believe that experience is restricted to material objects accessed through the five senses, for if so you will discount religious experience, or do you believe that there are other modes of experience, such as the religious mode? If so you will be open to what Buber, a well-respected Jewish philosopher, writing in I and Thou, describes as the presence-power of the divine in your consciousness.
If the latter, you are in good company, for you will be in accord with Rudolph Otto, whose seminal work on religious experience, The Idea of the Holy, was the first to treat religious experience philosophically. You will be open to William James, whose pioneering work, The Varieties of Religious Experience, was the first to treat the subject scientifically. This line was continued by Sir Alistair Hardy, a Nobel prize winning biologist, who founded the Religious Experience Research Unit, then at Manchester College, Oxford, who regarded religious experience as definitely non-hallucinatory and having positive effects in the lives of recipients. You will be in agreement with Roger Scruton, one of Britain's leading philosophers, writing in The Soul of the World, who locates religious belief in a response to the experience of the sacred; and you will be in keeping with the many mystics and ordinary people who have undergone a sense that they were guided, inspired and saved by a presence power that makes occasional manifestations in their lives, and which some feel is a constant background presence in their existences.
If you take the path of openness to the influence of God in your life, you will not have solved all your problems. Genuine faith is a stimulus to thought, not a lock on it. For me, my faith is not primarily a body of ideas, but it is a sense that I am influenced by something greater than myself. I find that membership of the church, community of belief, provides me with the conceptual language to think out my commitment. In effect, the formal beliefs, doctrines, are not faith itself, but the ways in which I express and think it out. But as I implied above, faith is a journey, the simplistic understanding of God gained in my Catholic childhood has evolved. I have not rejected, but deepened it. I have never seen God as a "Bronze Age beardy" as one atheist, who probably gained the bulk of his understanding of God from cartoons, described Him, but I now go along with the mystics who regard God as profound mystery, but very real. There is still some way to go.