@SP&DT stamp is the safest option. Depending on mistake and how observant airline staff is, you may or may not get allowed to board with error on GC. Considering, there's multiple times you'd be checked on the way to US, I wouldnt take the risk of getting denied boarding.
E.g if mistake is one letter in the kiddle name you may be OK, but if it's date of birth, or your name is John on GC and Daniel in passport, that's another story.