The first documented account is close to the place of birth.
Stig Waidelich was born on August 5, 1961 in the Kapiolani Medical Center in Honolulu, where President Obama says he was born. Monika Danielson is Stigs mother and she has vivid memories from the hospital after Stig was born. Monika told CNN that she remembers visiting the nursery after Stigs birth and seeing a lot of Asian babies, one white baby which was her son, and one black baby.
Because Monika is from Sweden, she told CNN that she had not seen many black children or babies before, which was why she particularly remembers seeing this black baby in the nursery. When President Obama became a candidate in 2008, Monika noticed his birth date and hospital in an article and remembered that day in the nursery.
http://cnnpressroom.blogs.cnn.com/2011/04/26/cnn-birther-investigation-no-doubt-president-obama-was-born-in-hawaii/
To backup her claim of few African-American births in Hawaii in 1961. There this table from 1961 of births by race of father and mother. Notice there is no category for Negro.
Thanks. That’s what I mean by evidence.