The problem with asking them to prove it is that they will spout off their interpretation of the Bible.
Some biblical literalists say 10,000 years, some say 6,000 years, but who is right? Perhaps they're both wrong.
Ask them this: Is your interpretation of the Bible equal to or superior to that of God?
Hopefully, that will stop them in their tracks. The point is that anyone's interpretation (even mine) is suspect. Only humility will help one find answers. Any good scientist will tell you this. Humility is key to any discovery.
As a Christian, I know that I don't know everything. I have found great wisdom in Buddhism, Taoism, Judaism, the Kabbalah, and even Scientology. As a scientist, I can appreciate the intricacies of the universe and in mathematics. Underlying all that apparent complexity is a beautiful simplicity to it. As an artist and a writer, I've learned to think outside the box.
All of these have helped me, with the proper humility, to find previously hidden wisdom in the Bible.
Ask them if they know that the timeline in Genesis has been found to be compatible with those of science. That Genesis now tells us that Noah's Flood occurred 27,970 BC, and that the first men and women (Adam) existed 10,434,130 BC. Okay, anthropologists have a little more digging before they find bones that old, but now they have plenty of time. They have biblical room to maneuver. ;)
On the way to finding this timeline, I discovered the Kabbalah's "Tree of Live" embedded in two chapters of Genesis. And most scholars I've read consider the Kabbalists to have been a medieval group. Some Kabbalists like to point out that they've been around since Adam. Well, it looks like I've found a kind of proof that pushes back their origins another 2000 years.
After finding this timeline, clues in those numbers led me to the real culprit behind Noah's Flood and the meaning of the "daughters of men" mentioned in Genesis 6. The culprit I found from studies of science. Imagine that!