Two-story building is not a requirement for civilization, of course. Supposely, the oldest were built after colonization and SSA never invented it before, but there are older houses. The oldest two-story building in West Africa was ocuppied in 10th/11th century and it is found on a site in Burkina Faso. It's called Oursi Hu-beero
The house had about 25 rooms, being circular or irregular (indicating that the rooms were added separately and not by different people of the same family/group, but there is also the pre-planning theory). The bricks are "irregular" as well (different size from other rooms unlike other buildings that were all circular or rectilinear), and the walls covered all of them (so it ended looking as a single structure). The superior floors were made with wooden timber/beams, coated with a layer of clay (20 cm thick), and was used as working place and daily activities, as well sleeping sometimes. Mudbrick pillars sustented the roof. The pottery is mostly local, but also foreign (some pottery was similar to those in Djenne and Dia in Mali, cities in Niger and Nigeria and other cultures around, they imported), and some objects found, like cowry shells, were imported (direct or indirectly) from the Indian Ocean, so they were part of tran-saharan trade. Maldives cowry shells were imported to the Mali Empire some centuries after. The house was fired in the 11th century and the local people probably slaughtered.
Digital reconstructions are shown in the book, but I don't want use the pictures here (copyright, you know), only those in the website. The TATA SOMBA houses are also two-storied houses from Benin with multiple rooms, but I don't how old the tradition is. This may implicate they may be old as well, Benin is close to Burkina Faso.
More informations in the book: Oursi Hu-beero: A Medieval Complex in Burkina Faso, West Africa (2011) by Christoph Pelzer, Lucas Pieter Petit, Maya von Czerniewicz
A link with some limited information of the structure:
Source: reddit post