Congratulations!
You'll need a substrate that holds more moisture. Baby box turtles need to be kept very moist. They'll stay submerged in the substrate nearly all of the time. "Forest" blends usually work well. They are typically smaller and more moisture retentive. Shredded and pulverized coconut shells, sphagnum moss, organic(and non-fertilized) potting soil, bed-a-beast, and rich soil from your pesticide free garden can all work. Some prefer to mix these together. Mist to maintain the proper moisture (close to egg incubation conditions).
Basking lights tend to dry things out. You'd probably be better off using UVA/UVB flourescent lights. They need UVA/UVB! Keep temps around 80 degrees F. You can set up a hot spot if you'd like.
Feed them daily for now. Earthworms, tiny superworms, roach nymphs, roly polys, slugs, waxworms, and virtually any other small insect that they can catch can be fed. Mealworms are just about worthless for baby box turtles. Vary the diet as much as possible. I prefer to supplement with vitamins and minerals at every other feeding. You can go and buy those disposable "Glad-ware" plastic dishes. I cut a small hole in the lid and feed the babies within...sometimes dry and sometimes in shallow water. When they start eating well and regularly, you can alternate in some chopped veggies...blended carrots, cucumber, and squash are usually the first taken by my hatchlings.
Young box turtles are often too shy to sit in a water dish. Don't rely on this for hydration. Substrate moisture is very, very important. Organ damage can quickly develop in dehydrated baby box turtles.
I hope this helps. Sorry for the long post. Good luck. There is a ton of hatchling care info. if you scroll back through this forum.
RMB described and provided photographs of a wonderful beginner's setup for hatchlings. You could easily divide a properly sized sweater box into 10 quadrats with some plastic and silicone sealant.