"a logic for why God must exist."
There is NO logic for WHY a god MUST exist.
Matter makes up less than 3% of the universe. In other words matter does not matter. Matter is insignificant. We just assume it MUST be important because we are made of it. No, matter is just residue from an event.
Why must there be a god? The sum total energy has been determined to be zero. No energy was required in the formation of the universe. There is evidence that proves the sum zero energy. If no energy was required it means that nothing was required to kick it off. It would normally happen of itself without any aid or push.
It is easy to get caught up when you look around and see trees, the sky, rivers and lakes, birds and mountains and think these wonderful things had to of been created by something significant. But no, everything is made up of fundamental building blocks. Essentially everything is hydrogen atoms lumped together in different ways which result in different properties and how light refracts off of them. There is nothing special about it.
Without stars there would be NOTHING other than hydrogen. The stars force hydrogen atoms together to produce the other elements. Stars form because of gravity. Clouds of hydrogen condense due to gravity. When gas condenses it increases in temperature.
Without gravity there would be nothing. The universe would be uniformly distributed with hydrogen if there was no gravity. Stars wouldn't form. We wouldn't result.
So some attempt to claim that god had to exist because gravity is set just right. If gravity were stronger than it currently is, our universe would be nothing but black holes. And if gravity were less, then stars would never form. This isn't true at all and it over exaggerates the window range that gravity can fall into to produce the universe as we know it.
I see absolutely NOTHING that suggests that a god MUST exist. Please show me where this thing is that does.