The reason this is critical for sickle-cell patients is that the gene mutation causing the disease is on the adult hemoglobin gene, not the fetal hemoglobin.
But shortly after birth, the body stops making fetal hemoglobin - its production blocked by the expression of the BCL11A gene - and starts making adult hemoglobin. Even babies with sickle cell disease make normal red blood cells because fetal hemoglobin doesn't sickle. All babies in the womb and newborns have a certain version of hemoglobin called fetal hemoglobin.