So try not to bug him too much so he comes out before he's ready. Once they slit, they still have to absorb the yolk that's left, and have their egg stem fall off.
Softening is a major prequel to hatching- now next time you'll know what to look for!
When he gets out, a basic hatchling check-up would include: check the belly to make sure the egg stem attachment site is closed. (If not, see the sticky in my personal forum here.) Gently but firmly feel his spine from head to tail, looking for kinks. There are a couple areas that can fool you; if the hatchling arches its back hard by bending over your finger and pushing back, about 1/4 to 1/3 of the way down, it can feel like a kink there. Then, when you run your finger over the spine right above the vent, you can feel a bump. Check to make sure he has both eyes (not an emergency if he does not) and that his jaw is fully formed.
I get a weight, then move the hatchling to his own bin right away. You would include a water bowl that won't tip. I use 3" ramekins- it makes a nice perch, too. Toilet paper tubes, flattened, make perfect hides. I keep neonates on paper towels- they like to burrow underneath or in the layers. You could also include a tiny pile of damp moss from the egg container.
The babies will go blue almost immediately, and shed in less than a week. I mist a couple times in that period, if I think about it, but they generally shed just fine if I forget.
Then you can feed right away after they shed, or wait a week for them to use up the yolk they have absorbed. It hasn't made a difference, to me. If you have trouble getting them to eat, there is a sticky about tricks down in my personal forum. The big thing is, don't try every single day.
Good luck! Nothing beats the fun of your first hatchling!!