Even when I put out clay or paints, my child won't come near or try to touch them. Are there ways to make it easier to join in?

Besides a lack of interest, they may dislike the sensation of dirty hands or the smell. First, consider even just watching as taking part, and let your child see an adult playing nearby. When they come closer, let them choose ways that don't involve touching directly — pressing on it through a bag, or using a spoon or brush. Don't make touching the goal; explore where along "watching, touching with a tool, touching directly" they can enjoy it.