There is no way to answer this question objectively or precisely as there is no definite way to differentiate between African culture and African American culture. Just as there is no way to say exactly when an immigrant becomes Americanized, we cannot say exactly when slave culture became African-American.
That said, I would argue that this change happened sometime in the first decade or so of the 18th century. The reason for this is that this is the time when the slave population in the Southern colonies of British North America became relatively large. When the populations became larger, and when they were concentrated on larger plantations, many blacks lived together and were able to create their own society in a way that was much less possible when they lived mainly among white people.
In the 18th century, there also came to be more and more slaves who had been born in the colonies instead of being imported. This meant that these native-born slaves could provide a basic foundation for the African-American culture. Even though new slaves still came in from Africa, they could be assimilated into African-American culture because that culture was built on a strong foundation of natives.
For these reasons, the early 18th century is the time that can best be identified as the point when Africans became African-Americans.