In his 1995, 2006 book, Dreams From My Father, Obama references finding a copy of his Birth certificate when he was in high school, as at p. 26 where he states:
"I discovered this article [story about his "father" in the Honolulu Star-Bulletin], folded away among my birth certificate and old vaccination forms, when I was in high school."
At some point in time he did have a birth certificate.