My dh teaches pottery in the adult/community education program (also a hs pottery teacher). He allows children to take classes alongside a parent, as long as the child is mature enough to actually sit and do pottery for the length of the class. That might be an option to explore. Or are there any local studios that offer pottery classes for children?
The thing with clay/pottery is, there are some really big supplies that make it inconvenient to explore without a pottery studio. Like a kiln, a high quality wheel, and expensive glazes. But if you have some land, there are other firing options. You can fire some kinds of clay in a fire pit, or in a metal trash can.....dh knows how to do these things, but I don't, lol. And there are lots of ways to finish pieces other than glazes....and techniques that do not require a wheel (slab design, pinch pots, coil).