It is true that human reason reaches vastly beyond what is needed for hunting a mammoth, or even for handling more complex situations arising from social behavior and language.
Sure, a lot in nature feels counter-intuitive, but this doesn't preclude us to tread on such ground. The grasp of the structure of space by Euclid, for example, was so firm that he even singled out the axiom, which is problematic (the parallel postulate), as problematic (obviously, he still used it, but avoided it when possible). And this is only the beginning, if we think about the upper reaches of theoretical physics and mathematics.
But I don't see how all of this gets us to a theistic God, who is conceived as an all-powerful and omnibenevolent Creator of the Universe.
It would “only” be an argument against the modern worldview of the contemporary secular elite which is based on physicalism and Darwinism.
By this, I don't mean the crazy idea that Darwinian evolution would turn out to be totally flawed (= has no explanatory power or gets the facts seriously wrong) – it suffices to be incomplete (similar to classical physics). Rationality might in part have immaterial features (so physicalism would be false) and teleological processes might exist in nature (very broadly speaking), which aim at the development of rationality.
Such kind of atheistic worldview might feel odd and unsatisfactory, but that seems to be rather a result of our cultural biases, which we should strive to overcome. In India, they never had those big troubles about such proposals:
Śāntarakṣita and Kamalaśīla also point out that when there are no composite objects in this world, how can there be an Intelligent Being who is supposed to produce them? It is like proving that an ant-hill is the creation of a potter. Even objects like houses, stair-cases, gates, towers etc. are made by persons who are many and who have ﬂeeting ideas. If the opponent means only this that all effects presuppose an intelligent cause, we have no quarrel with him because we also maintain that this diverse universe is the result of intelligent actions. We only refute his one Intelligent and Eternal Creator.
Chandradhar Sharma: A Critical Survey of Indian Philosophy
NB: the ant-hill of the Indian harvester ant looks like a clay pot.