How can I prove to my atheist professor that God exists?

Kill’em (Just Kidding!).  Short of your professor being convinced by the arguments of brilliant minds like St. Thomas Aquinas or Bernard Lonergan, S.J., there is little we can do.  (Personally I love the argument from contingent being [that which can not exist].  Such being must be kept in existence by a necessary being [that which cannot not exist]).  Still, there is really no sure way to logically or philosophically prove God exists.  All the arguments founder on the meaning of words, and the acceptance of certain presuppositions.  I think the question, “Why is there anything rather than nothing?” is a great question.  Some philosophers tell me it is a pseudo question.

At some point you stop trying to convince people God exists.  You just live your life in a way that demonstrates you believe God exists and loves us.  God has to then use your witness to touch the heart and mind of the unbeliever.  We don’t have to convince or save people.  God does that.  We are only God’s helpers.