Birth Certificate/Passport - Oregon

Hollally

We are traveling out of the country in February and are working on getting a passport for Q. He is one month old. I received his ss card in the mail yesterday but do not have a birth certificate for him yet. All we have is the hospital certificate. Can anyone tell me how long it took to get their birth certificate for their LO? Is there anything I can do to speed it up? I completed all the necessary paperwork in the hospital. We are in Portland, Oregon.