Yikes! Doesn't sound good. No free food? It's a six hour flight! Delta are not a budget airline, I expected complimentary food and beverage would be standard. I've never known a full service, scheduled airline to charge for meals.
Welcome to our world.
Airlines in the US stopped serving complimentary meals on domestic flights a long time ago. They sometimes offer food for purchase on board, but I never partake. I'm too cheap.
You can indeed bring your own food in. Lots of people do. Most airport concourse food vendors are equipped to pack up food "to go".
Note the expression "to go" which is the American way of saying carry out or take away food. "I'd like that sandwich to go, please."
My suggestion is to bring food along for your child, something you know the kid likes. The adults can eat a hearty meal before getting on the plane and just wait it out. You will have airplane food on the over-water international segment.