The problem with any sub-saharan empire is the utter lack of seagoing vessels. All the potential candidates are land-focused -- be they Ehitopia, Mali or Ghana. And even if they would manage to control significant amount of territory north of the Sahara (which might even be possible with a wanked Mande Empire e.g.) - the jump north would be a giants leap for their logistics. Especially since the focus and center of this hypothetical realm would most certainly be in the south.
In order to fulfill the challenge (outside of some Nubian workaround) the empire needs maritime focus and the technology to build seagoing vessels.
So a slightly gamey attempt:
1. Early Malian Empire conquers the coast to the West with higher priority.
2. T
he Vivaldi Brothers (1291) actually reach Tekrur or whereever and are brought to Niani as a curiosity.
3. They stay and their galleys remain known, some of their tech, e.g. crossbows (which they most likely carry), are adapted.
4. The Malians focus more on the west because of that -- historically a very underdeveloped region in their empire.
5. Because of this focus they invest in bringing Arabian naval professionals into the empire (a bit like what Mansa Musa did with scholars for the university of Sankhore)
6. Malians with Sea Going vessels that develop into a Caravel-like way (which isnt an unlikely development from the dhow technology the TTL Malians would have access to)
7. Mali becomes devolved (very likely with their structure if they dont outright collapse), the West becomes naval focussed trading state.
8. Mali beats the Portuguese to Madeira (historically settled after 1420) -- which technically isnt Europe I guess, but is good enough for me.
(we can always have them set up a small outpost on the Azores at this point, and thats geographically on the Eurasian Plate, so I'd argue Europe)
9. Mali goes colonial. The fewer dreams of Abu Bakr II beome real and variola minor (the way less dangerous smallpox variant) makes its way to America - alleviating one of pre-1900s most reviled historical tragedies.
10. To mess with the Euros even more, there is now a filthy rich naval power blocking their way south and towards the Cape.
From this point onward... there really is everything on the table
Edit: The Genosese being Merchants they are they certainly had some economic knowledge. This is also right at the edge of the invention of double-entry bookkeeping. Now we have Malians with natural currency and the baseline to develop a banking system. This will require new industries like paper making....I kind of feel like resurrecting my hopes on a Malian TL with this rough premise.