I seem to recall a philosophy text saying that "What is" questions eventually layer down to "facts"- at the most basic level things just ARE.
"Explanation" always involves comparing and matching patterns: for example some people compare the sound pattern "God" with the concept pattern "math-logic of the Universe".
Why talk of God influencing things? Consider the statement "Things are." "Things" here is of course, things. "Are" here is Existence = Love =God according to Catholic theology.
That makes sense because if you don't dictate to someone, and let them be; that's love- so God lets us be, loves us, and we ARE. He gives us so much freedom, so much 'elbow-room', he gives us our very elbows.
It is a mistake to try to subject God to space-time; God is outside space-time. Spiritual beings exist and play with patterns outside space-time.
On a personal note; the 'telecommunications agency' that allowed me and my newborn twin to know what each other was thinking (thinking without verbal labelling of language) appears to be WHO humans call God. The exhilaration of being alive as a newborn baby (who lives in two non-material dimensions of Soul and Spirit as well as the physical dimension of Body) - this joy of aliveness involves an awareness of the Creator living in me and I in the Creator. (Hopefully I shall re-align the patterns of body, spirit, soul and regain teleportation/ telepathy abilities etc. some time!)
Why expect God to 'influence'? God made you: your move! You influence. God is Existence; makes the great cosmic game possible. You are the player. There might be other beings in other galaxies who would much like it if the lost human race would re-join the rest of the folks in the Universe in the wonderous cosmic game being played out there. Who knows?