Let me see if I can address these two together:
I would have to say that personally, I came to "know" God without ever "believing"...and then, in time, came to believe. I have seen...
blessed are those who have not seen and yet believe.
I am not sure my whole testimony was what you were asking me to explain, but briefly: I had, over many years, spiraled down through being a victim of crime, going through bankruptcy, loosing my marriage and peaceful contact with my children, etc., etc., to a point of realizing that I was in the very place where people commit suicide. The last straw came and one night while lying in bed, I started talking to a god I had no knowledge of, merely tidbits and rumors. I told him if he wanted my life he could have it, but he would have to take it, otherwise I needed some answers. I needed to know what life was about and what my part in it was...or, it would be the only thing that had not failed me, I would go live in the woods. That's what I said. And he answered.
I was immediately taken up into the atmosphere directly above the place in the woods I had threatened to go...where he showed me my place in the world, my purpose for living. In an instant I was back in my body, and I shot straight up and didn't stop until I was seated at the foot of my bed. I broke out in a cold sweat and sat there in bewilderment, yet "knowing" better than to question what had just happened...I "knew."
Within a week my life completely changed. I was changed. My job changed, my relationship broke off, and I moved. I landed at my brothers house where I found a bible in the spare room where he put me up. I read it from cover to cover, from one point of confirmation of my experience and answer, to the next. The one thing that was unavoidable and undeniable, was...the Author of the bible, and of my experience, was without question, the same. I "know."