Another Birth Certificate Question

My husband and I are adopting our daughter through the county children services. I asked if I could have a copy of our daughter's original birth certificate. She has lost so much in her five years that we wanted her to have the certificate as a keepsake. Anyway, our agency said no way. After we finalize, we'll get the court b/c copy with OUR names listed as her parents. I think this is so wrong. My question....is there a way to get our daughter's original birth certificate before the records are closed? Thank you.