But, that explanation is replacing your old beliefs in God with something new. Somehow you arrived where you are in Buddhism.
What kind of theism did you leave?
How long afterward did you find relevance with Buddhism?
I don't feel that I took something (belief in god) out of a particular file drawer in my mind and put something else in that drawer. That analogy just doesn't make any sense to me. I didn't fill a sort of void left from that old belief with another belief - I came to a very different understanding of life and the universe which has no need for anything in that position, or drawer. I'm not even sure that drawer exists now (analogy bent way out of shape here).
I was raised in a sort of generic mid-American WASP background. We went to a Christian Science church, but were not strict regarding that sect's beliefs.
I basically dropped most if not all belief in god as postulated by Christianity in my early to mid teens. I began practicing Buddhism when I was in my early twenties. My conceptualization of the universe and how all life, including mine, fits into that continues to evolve.
BTW, Buddhism is a practice, rather than a belief system. You can believe in Buddhism all day long, and nothing will happen if you don't practice. Conversely , you can practice without any sort of belief, as I did, and see results from that practice.