The only thing I can explain is my personal experience. Your feelings and beliefs, like mine, will continue to change throughout your lifetime as you gain new information and understandings!
That said, I was raised Methodist. I started out with strong roots in religion.
When my thinking mind was awakened, I started questioning everything. Like you, I came to the conclusion that God does not exist. I became an atheist.
I continued to inquire, like you are now, skeptically though, into every type of thinking. I had a hunger to know and understand everything but wanted not to believe it more than I wanted to believe it.
Despite that fact, unanswerable questions, the help of the beliefs and understandings of some of the world's brightest minds, and understandings gathered by my own personal experiences led me to become agnostic. I understood that there was something there beyond the explanation of religion but also beyond the explanation of my inquiring mind. I didn't know what and I didn't claim to know. I was extremely humbled in the presence of this great "something" which could be felt by all but explained by none and that I understood to be bigger than reasoning and induction could ever reach.
I continued to explore, investigate, I did everything I could to satiate this gnawing hunger in the back of my mind, my heart, to understand what was going on. Why, if I knew empirically that God did not exist, did I keep coming back to the question of "his" existence? Why did this feeling plague me almost constantly that I was wrong? One might argue that it was my socio-cultural surroundings and mindset that led me to feel this need to know, but I would contrarily argue that I had so rejected that society that I would much rather NOT have brought up those questions. I would rather have stayed ignorant in my thinking mind than conformed to those feelings. Yet I was compelled to do so and found myself at every moment following that feeling in the back of my mind that I had somehow missed something essential; even as I spoke the words, "I'm agnostic," a twinge in my heart whispered, "No, you're not."
So after years of questioning, seeking, learning, experiencing, and on and on, after years of being disappointed by the results my mind had produced, I logically tried a different way to figure things out and trusted my heart. I gave into my feelings, which is very scary at first, especially to someone who puts so much faith in knowledge, science, inductive reasoning. But once I was able to do that I found not an explanation for everything, but rather an understanding. The difference is that an explanation comes from the thought process, logic, whereas understanding is an innate knowing from within. I understood that God is in everything, everything is connected, we are all (dare I say) Love (not scientific "love" designed to generate reproduction, but the Love in which everything is created, thrives, exists).
Once I gained that understanding, I found that I could return with my mind and think through what I now knew, and-- shockingly-- it all made sense. It all lined up. Thankfully my knowledge and Knowledge were perfectly complementary.
And it is an ongoing process of gaining greater insight and checking it with my thoughts. I don't dogmatically go with my feelings, rejecting completely science and logic. The greatest part of it is realizing that science and logic are a part of the whole, not the whole. They are an integral part of the greater picture but ultimately they are not the greater picture. But since they fit in, have their place, they can be utilized as a tool to understanding Truth.
My spiritual journey has been rocky and long and will never be finished. I hope my story has inspired some more questions and thoughts for you!