I empathize with their question about proof for God's existence. I think that one of the best places to begin looking for proofs of God's existence is through nature. Every dimension of the human body, for example, is so complex and detailed that it is almost impossible to imagine that a random act of nature brought it into being. The Chazon Ish discusses the human eye and its delicate complexity and how, if looked at carefully (pun intended!), it points to a Divine source. It is not just the human body, though, that points to God. The whole tapestry of the natural world that we inhabit is one enormous proof that it was created by God. From the interaction of the stars and planets in our galaxy, to the minute details of the grass and the clouds point to a Creator. The Talmud discusses the fact that God is the only entity who can create - "all" we can do in this world is re-create using pre-existing material that was put in to place by God. One of the most basic tenets of Judaism is that God is the only Entity who can create something from nothing.
However, I personally find the strongest proof that there is one God who created the world, took the Jewish People out of Egyptian slavery and gave us the Torah at Har Sinai to be the proof from the Rambam. Look at the way in which the Torah was given to an entire nation "in person" (Deuteronomy 5:4), a Torah which teaches about the Creation along with everything necessary for life in this world and the next.
The Sinai experience has been passed down from father to son, from generation to generation until today. It is the same history and teachings that are transmitted yearly at the Passover Seder, and daily in study halls throughout the world. This is the testimony of an entire people to the truth that they experienced thousands of years ago that there is one God who created the world, Mankind, gave us the Torah and is eternal.
I think that you should suggest that they read one of the classic books of Jewish philosophy called the Kuzari which is a book written almost a thousand years ago by Rabbi Yehudah haLevy in the form of a dialog between a Rabbi and a Gentile king. It is theological debate between a Greek philosopher, a Christian, a Muslim and, finally a Jew. It is truly fascinating. There is an excellent new translation (with footnotes) by Feldheim Press that ought to be easily available.
