Along with piano or another instrument for reading music, just sing. Folk songs, regional and storytelling songs, old songs, musicals, hymns, ballads. How about rounds? Excellent ear training! Leads to singing parts well. Do you play the piano? My dad used to play songs with us singing while dinner was cooking. I don't have a good voice, but I have a vast repertoire and I know all the verses lol! Voice lessons can wait...DS (my theater major) started in high school, though his "competition" started in middle school.
A church in our town has an amazing youth choir program, that spends a lot of time on development and theory. So at least half the choristers are not members of the church, they are there for the training (and it's free!) I wish I'd know about it when my kids were younger. The high school choir teacher can always tell who came out of that choir. But your child can also maybe do summer theater programs or a summer community musical. Our community theater does musicals with room for kids as well as adults, and the kids learn a lot just by exposure to the amazing talent.
