I'd say the best bet would be via the creation of a centralized state centered around the vast expanse of the Niger basin. The state would start small, unified by a common culture which was vague enough to accommodate assimilation. It would begin as a hydrological empire, whose monarchy depended upon mass cultivation. Its economy would be largely agrarian, centered around the mass cultivation of durum wheat and millet. The state over the centuries invested much of its income towards the maintenance of a sophisticated irrigation network. This in turn supported a large population, an enormous military, and a network of mercantile cities.
Said kingdom would expand via diplomacy, conquest, and colonization. Its culture would be accepting of integration, even as its citizens out number those of conquered lands, while assimilation absorbed the peoples of rival kingdoms and tribes. A bureaucracy is formed and expanded inorder to manage its vast expanses, while a pan ethnic aristocracy emerges its provinces and sub provinces. On the other hand, the cities are largely dominated by a merchant elite whose leaders control the trade routes to North Africa, Arabia, Europe and beyond. They return providing wares, and telling stories of the empires and kingdoms of the north, all of whom are but a pale shadow to them by comparison (despite being very profitable trade partners).Their expansion takes them to the coasts. Ocean going is slow initially, however as urban centers take route along the coasts, fishing techniques become increasingly sophisticated and over time sea faring evolves.
The state eventually reaches its natural borders. Europe see's it less as a state than an empire or nation, it controls nearly the entity of west Africa. It comes to be seen as a powerful, wealthy, unity state, spoken of in the same way as Rome or China. Its mercantile community assures that it remains prosperous and in touch with the advances of the outside world. Therefore said state remains comparative modernized, allowing it to maintain technological parity with its rivals. Its only a matter of time, before it begins to challenge the thassalocracies of Europe for control of the oversea routes. Therefore said state produces a large, well fed, and prosperious population, ready to compete with the west at its own game.
