My mom is amazing and my dad is. I think a way you could make your child feel more safe to come out to you is to be inviting. Don't randomly say, “Oh, don't become trans” and that random stuff, because that's not inviting at all.
When I came out, I first told my mom because she showed me somebody who was non-binary who she thought reminded her of me, and that invited me to come out.
I think that you should just be with your child as they go through stuff. Just be with them as they do their growing up.