“Is there a conclusive argument for the existence of God?”
Sadly, there is no conclusive argument either for the existence of God or anything else. The reason is unbelief. Perhaps I should not use “reason” and “unbelief” in the same sentence. They are in fact mutually exclusive. The unbeliever refuses compelling arguments, persuasive evidence, and even the science he claims to worship when any of these do not agree with his predetermined position.
For such a man, literally nothing is ever conclusive.