I will try to present some reasoning why an atheist might believe it is "logical that something uncreated ended up with earth containing organic intelligence."
Assume we have a creation event. That would be a first cause. What happens after that are called secondary causes. Here is Wikipedia's description of secondary causation:
Secondary Causation is the philosophical proposition that all material and corporeal objects, having been created by God with their own intrinsic potentialities, are subsequently empowered to evolve independently in accordance with natural law. Traditional Christians would slightly modify this injunction to allow for the occasional miracle as well as the exercise of free will. Deists who deny any divine interference past the creation event would only accept free will exceptions. That the physical universe is consequentially well-ordered, consistent, and knowable subject to human observation and reason, was a primary theme of Scholasticism and further molded into the philosophy of the Western Tradition by Augustine and later by Aquinas.
If the creation stops then the universe is on its own except for occasional miracles when the first cause intervenes. Note how Deists push out God's action by eliminating miracles.
Atheists can claim, based on a belief in secondary causation known through natural laws, that either the universe is eternal and doesn't need a first cause or if it did begin (such as believed with the big bang) the cause was some sort of randomness.
Just as the atheist denies a first cause a theist could deny secondary causation or reduce its significance. A complete denial of secondary causation is viewed as continuous creation or occasionalism.
Occasionalism is a philosophical theory about causation which says that created substances cannot be efficient causes of events. Instead, all events are taken to be caused directly by God....The theory states that the illusion of efficient causation between mundane events arises out of God's causing of one event after another.
So to go back to the original question:
I’m not asking if it can be true. I’m not asking how it can be true. I’m asking why is it logical that something uncreated ended up with earth containing organic intelligence.
When theists accept secondary causation (except for some miracles) they open the door logically for atheists to believe only in secondary causation. They make it possible to think in terms of only secondary causation. If God created the world at the big bang then everything after that (except for miracles) would be done by secondary causation including organic intelligence.
The way around that would be to present a theism that limits secondary causation or entirely eliminates it in some form of occasionalism.
Wikipedia contributors. "Occasionalism." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 9 Sep. 2018. Web. 20 Mar. 2019.
Wikipedia contributors. "Secondary causation." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 8 Apr. 2018. Web. 20 Mar. 2019.