What are three reasons why Descartes proved God's existence? What did he solve by proving it?

In his 1641 treatise, Meditations on First Philosophy, Descartes lays the groundwork for his theories that appear in later works, including his Principles of Philosophy. To fully understand Descartes’s philosophies, it is critical to consider the significance of his education, which consisted largely of mathematics and science. Consequently, he rejects proofs that result from senses and perceptions (e.g., miracles, bible stories, etc.). Descartes’s attempts to prove God’s existence are part of his vision for a new philosophical system based on mathematical theorems.
Firstly, Descartes uses Euclidian geometry to formulate his proofs. He does this because Euclidian geometry has an axiomatic methodology, meaning that there are fundamental truths which are used to derive all deductions. Furthermore, he wants a logical system of proofs beginning with a premise, followed by careful steps using deductive reasoning to arrive at solid conclusion. He believes this method will create precision within the philosophical realm.
A third reason for Descartes’s desire to prove God’s existence lies in cosmological reasoning. Cosmology includes the theory of design, which states that systems within the universe could not have happened merely by chance. Therefore, Descartes wants to show God exists as support for the aforementioned theory.
At the time, during the Age of Enlightenment, Descartes was hoping to solve ongoing arguments regarding the creation of the universe and God’s existence. Unfortunately, many of his theories, or axioms, were disproven by theists and atheists alike.
https://plato.stanford.edu/entries/descartes-ontological/