You are right... 'no sooner than' does not work in that sentence. Never has the world seen the like of.... (yes, you are correct, this works fine, grammatically). For emphasis you could say, Never before has... But are you sure it should be HAS? We'd need the text, but are you sure it should not be, Never (before) HAD the world seen the like of Alexander... If this is a history book, referring to the time of Alexander.... shouldn't it be HAD? Example: (referring to the Roman Empire and the year 60 BCE (BC)) Never HAD the people seen the like of him. Many now decided to support him.

"Never before has the world seen the likes of Alexander the Great, a philosopher king" would be a better sentence.