This is my first time hatching eggs. They just hatched today. I went ahead and moved them from the incubator to the brooder, because they were dry, and it is plenty warm.

I was just curious when I can let the kids hold the chicks. I was thinking it would probably be fine, but I might make them wait a day or two. Thoughts?

We handle them immediately. Sometimes we even have to help them hatch. Chicks are either going to live or going to die. Your handling them isn't going to hurt much other than chilling them. Handle them to move them but don't make an hour long petting zoo out of it. Get them back to the hen or brooder quickly. We've done hundreds over the years like this whether hatched form hen or incubator and it doesn't make much difference.