All Christians should understand that they cannot prove God. It is impossible, but we can do is attempt to provide what we believe to be evidence of Him. God is the one who proves Himself to each person, it is not something that we do.
My argument for God is:
Do you exist?
Is it possible for you not to exist?
If it is possible for you not to exist, but you do exist, then you must have been caused to exist.
You cannot bring yourself into existence, since something must exist first in order to bring something into existence. It is illogical for something to exist and not exist at the same time.
Something must have caused the beginning of life to exist because there cannot be an infinite regression of causes. In order for something to cause the beginning of existence, there must have been a first cause.
An infinite regression of causes ultimately has no beginning, which means that there would be no beginning of exist.
Since we have life and exist in a existing universe, there must have been a first cause or beginning to exist.
Therefore, there is an uncaused cause of all things that do exist.
The uncaused cause, or beginning of life, and the universe is God.
God is eternal; therefore, uncaused.