The Rouffignac cave in southern France has evidence of children's art. The cave is estimated at 13,000-14,000 years BP.

There's a type of prehistoric cave art called finger fluting, which refers to the lines left behind when a person runs their fingers across a soft wall within the cave. Here's what it looks like in Rouffignac: https://upload.wikimedia.org/wikipedia/en/0/07/RouffignacFlutings.jpg

The archaeologist who did this research found that children aged 3 and 5 were responsible for a great portion of the flutings within Rouffignac. You can find a great article on her findings here.

This is an earlier study done by one of the archaeologists who worked on the current research. This research was where the methodology for the 2011 research came from.

In the above study it has been noted that there are arguments for even older prehistoric children's paintings in Australia, from a cave dating to at least 30,000 years ago. However, the Rouffignac cave is the only confirmed with this methodology.