The mother is going to have to file an I-130 for her and process that inside the U.S. Then an appointment will have to be made a the U.S. Embassy or Consulate in the country where she is from. The child cannot get legal status without leaving the U.S. unless it can be proven that she entered the U.S. legally. Luckily, as long as the child does this interview before turning 18 and a half (meaning she leaves the U.S. before turning 18 and a half), she has no penalty to come back. So conceivably, she could leave the U.S. for a few short days and come right back after approval and enter the U.S. as a Lawful Permanent Resident, then the mother just has to file an N-600 for her to get a Certificate of U.S. Citizenship. Here is an official link on how to start the I-130 process:
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