There is a great tradition of finding evidences for God and reasons for the existence of God. it was all the rage in the Middle Ages, Thomas Aquinas and Duns Scotus among others. It was part of a training in theology for ministry. Some of it was to confront the infuence of Aristotle and the idea of a static everlasting universe.
AsI have been studyingthe works of Duns Scotus I can highlight the Scotus “proof” which is a complex one that started from the argument of a First Cause of all other causes. Secondly that wthe First cause is also a Fiinal Cause, that moves things to an end. The Final cause is the reason for the First Cause to act. Thirdly, that there is something most pre-emmiment and most supreme and that this First, Final and Pre-eminant existing thing is also Infinite. Scotus actually uses Aristotles ideas against Aristotle by using his categories of causes to show there was a begining of things, a creator.
Such argmunents from causation etc may not hold quite the same authority today but they do remain a kind of critique of atheism. William Craig Lane has written on the subject and he has a website. There is also “Nature is not enough” by John Haught (a Catholic critique of atheism) and Richard Swinburn has also written defenses of the idea of God and Christian truth.