I don't know why you condemn the Great Man theory while talking about Alexander the Great and Genghis Khan -- two of the clearest-cut examples of how the Great Man theory isn't entirely wrong.
I'm not going to discount Alexander's successes. From all sources, he was very talented, if impulsive, cavalry calendar
Greece's climate and proximity to the coast made it one of the wealthiest areas in the world at the time due to exports of olive oil and wine. This allowed the free citizenry to be outfitted with the finest armor available at the time. That the Hoplites were free citizens, and not slaves, endowed them with a greater amount of morale than a number of other militaries at the time. Also, I believe his father was the one who created the phalanx formation. Put simply, he inherited the greatest fighting force at the time while being extremely well-funded.
The Great Man theory isn't entirely wrong, Napoleon springs to mind as another person who had an outsized influence on history. It's just that much of the history taught in US schools is about singular individuals and dates. They don't really go into the overall conditions of the times and that history is also the result of the decisions of everyday people like you and I
All too often, we are taught in school the great man, big event view of history, like Alexander was some superhuman solely responsible for the creation of his empire (No one ever brings up the biggest, the Mongol Empire).