It takes a lot of energy and effort for a chick to escape its egg, so for the first 12 hours a chick will rest and recover. By 24 hours after hatch chicks become much more active, investigating their surroundings and darting in and out from underneath mama hen.
How did the chick get out of the nestbox and separated from the broody hen? Can you send a photo of your hatching setup? Do what is required to make sure it cant get away from her warmth. If its cheeping loudly, that may mean its cold, but hopefully will warm up and quieten down soon.
As far as introducing older chicks to a broody that has hatched her own chicks, ive done that many times. The key to 100% acceptance is give the feedstore chicks to your broody before she ever takes her own chick(s) out of the hatching box for the first time. Once she sees her own chicks she hatched, she may reject the feedstore chicks as unwanted intruders. When you are sure all viable eggs have hatched, remove the remaining eggs and give the feedstore chicks to your broody at night. Put the feedstore chicks behind and underneath her tail. Do so in complete darkness except for a small flashlight. Her own hatchees & the feedstore chicks will snuggle together all night, & in the next morn be good to go. I have used this method with broodys that would otherwise Not accept chicks they didnt hatch, & have introduced feedstore chicks up to 3 weeks old.