It’s a difficult thing when someone we care about suffers from depression or other mental or physical illnesses.
The truth is, you cannot convince him to do anything.
It’s difficult when we are dating someone, investing time and emotion in them and their wellbeing, and they have something seriously wrong inside them. What you need to understand is that you are dating, not married to, this young man. Dating is a discernment process. In that process part of the purpose is to determine if there are things that preclude marriage to this person. You may have found not one, but two: chronic, untreated depression AND his lack of religion.
Again, you are NOT married to him, and you should not move forward with any such plans. And you should consider that this is not the right person for you. He may not be the right person for ANYONE until and unless he deals with his issues.
Many young people who date make the tragic mistake of believing the other person is their responsibility, that they are somehow “abandoning” or “giving up” on the person if they move on past the dating relationship. That is too bad, because such reactions misunderstand the purpose of dating and discernment in its entirety.