Yes I would think that you could get a gate pass, although I would first call DL to a, find out and b, see what you need to bring to get a gate pass, then I would get to the airport early to go through the hassle

howeve I wonder why wasn't the child at least given notes in english as to provide to aircraft, ground, someone else for help if needed. This doesn't sound like there were very responsible parents or guardians sending this child. Why didn't they arrange in advance for you to meet them inside by providing you with gate pass info?