I don't think knowledge and faith are two contrary things. In other words, I can have faith in God but still know him and know that he exists.
This seems to me to be the clear teaching of Scripture:
Matthew 9:6 But that you may know that the Son of Man has authority on earth to forgive sins”—he then said to the paralytic—“Rise, pick up your bed and go home.”
Jesus' miracle was able to give those who witnessed it knowledge that Jesus was the Son of Man (this is a messianic title: see Daniel 7) and that Jesus, as the Son of Man, had the ability to forgive sins.
Matthew 11:27 All things have been handed over to me by my Father, and no one knows the Son except the Father, and no one knows the Father except the Son and anyone to whom the Son chooses to reveal him.
This verse clearly teaches that those to whom Jesus reveals the Father
know the Father.
And to Jesus' disciples he said:
Matthew 13:11 And he answered them, “To you it has been given to know the secrets of the kingdom of heaven, but to them it has not been given.
Again Jesus said,
John 8:31–32 So Jesus said to the Jews who had believed in him, “If you abide in my word, you are truly my disciples, and you will know the truth, and the truth will set you free.”
In fact, saving faith is spoken of as knowledge in Scripture:
John 17:3 And this is eternal life, that they know you the only true God, and Jesus Christ whom you have sent.
If you have eternal life (if you are saved) you know God and you know Jesus Christ.
And this knowledge isn't something that is contrary to having certainty or great assurance about either. Thus, Luke wrote his gospel "that you may have certainty concerning the things you have been taught" (Lk 1:4).
And when Jesus rose from the dead "He presented himself alive to them after his suffering by many proofs, appearing to them during forty days and speaking about the kingdom of God" (Acts 1:3).
So we shouldn't treat faith as being opposed to or contrary to knowledge and we shouldn't treat faith as being something that is irrational or somehow outside of reason.
I would strongly suggest the book "Longing To Know" by Esther Meek. It's not too big and it's an easy read and, from what you've said, might be exactly what you're looking for.
(P.S. The book doesn't try to give proof for the existence of God or anything like that. The book is simply about what it means to know God and how it is that we know God (or know anything at all).)