Most modern archaeologists and geneticists agree that the whole human race originated in Africa.
From a more recent perspective though, no. Not all Blacks come from Africa. Just because someone's skin color or features look similar to those of Africans. doesn't mean they or even their ancestors come from Africa.
Do research on the Dravidian People of India, countries in the Caribbean such as Puerto Rico, Dominican Republic, Jamaica, Trinidad, Cuba, etc., the Aborigines people of Australia. The list goes on and on.
Yeah, some of those people may have features very similar to Africans, but that doesn't mean they are classified as having African descent.