This is a question I've been asked as well as asked of other people. But the answer I give or someone else offers doesn't matter because our answer doesn't change if God does or does not exist. Our belief/trust in a deity doesn't change the existence of that deity. Just like my belief or dis-belief in the Grand Canyon doesn't change the existence of the Grand Canyon (I've never seen it in person, only in picture books so I don't have "eye witness" proof of its existence).
I have found that I have moved away from using this question in my conversations with people. I tend to ask questions that are more along the lines of
"How should people treat each other?"
"What values do you want your life to have?"
"How can life be experience if justice & forgiveness were a part of everyday convictions?"
"What is love & how can it be genuinely expressed?"
My faith framework says that our lives can only be truly lived fully following the convictions/standards of Jesus because His call to humanity allows faith to be lived out in action, not in the "right answer" to the God question (Mark 10:16-22).
I believe I want to see action matter much more in our lives of faith than the appropriate answers. If I believe God exists I can say so...but I also need my life to align that way. ALL of my life--Not just certain compartments of my life. I want it to be HOLISTIC.
"Radical Amazement" is a term I like. I like the radical amazement people have when they realize the life they can live with as Jesus leads. I love seeing students wrestle with convictions & make conscious decisions that their life MUST align with Jesus if they are going to claim relationship with Him.
On a week to week level I tend to experience that I get more questions asked of me as to why I live a certain way, parent a certain way and have certain convictions rather than "Do you believe in God?"
I think people tend to take notice of my actions. Hopefully my actions answer the "God question" before they even ask it.