Where he was born, they don’t have birth certificates.........
At the time Obama was born, Kenya was a British colony. I believe most of the records were taken to the UK when the British left. But I don’t know if that would include Kenyan birth records, although I’ve seen it said that it would.
Probably no record was kept for a lot of African births, but Obama senior was a prominent man, chosen to receive a scholarship to Harvard, and most likely records would have been filed and kept.