Whether or not you can do handbuilding without a kiln depends on the type of clay you use. If you are working with a self-hardening clay, you can let it dry overnight instead of firing it. There are also kid-friendly polymer clays that you can bake in the oven. The downside of these types of clay is that uses of your ceramic piece will be limited. You will not be able to eat or drink out of this type of ceramic piece.
If you are handbuilding with earthenware clay, use a kiln to fire it. Ovens do not get hot enough to fire earthenware ceramics, and if you’re not careful, baking the clay can cause it to crack. Depending on your project and clay type, a kiln can take about 8 hours to heat up to about 2000 degrees Fahrenheit, and an additional 12 hours to cool down.