In other words, could anybody have done what Alexander did? Or did he have innate talent?
I know that questions like this are often difficult to answer when considering the past 200 years, let alone 2000+ years.
The question of his innate talent in relation to the extent to which he benefited from what he inherited from his father is often debated among today's historians. First off, it must be said that Alexander's father Philip took the tactics that he learned from Epamindondas while he was a hostage in Thebes and adapted it into his Macedonian army to form an incredibly disciplined army that revolutionized warfare in Greece. To quickly summaraize it revolutionized warfare with the substitution of the spear which was about 7-8 ft. with the sarissa which was 18 feet and allowed multiple lines of spears to extend beyond the front line to confront an enemy phalanx. Philip was able to train an army disciplined enough to handle this cumbersome weapon in formation in unison with one another and at the same time, developed a cavalry that would act as the decisive blow that would strike the enemy flank while the phalanx pinned down the enemy infantry. This "hammer and anvil" tactic is still used today just replace the phalanx and cavalry with a platoon of riflemen and and airstrike/artillery strike. This cavalry was especially impressive because they were able to attack with impressive charges despite not having saddles. This is the army that Alexander inherited at the age of 20.
Despite his accomplishments (the conquest of Greece), Philip is overshadowed by his son. While I believe that Philip would have defeated the Persian Empire, I don't think he would have gone as far beyond that as Alexander did. I also think he didn't have the charisma of Alexander who was able to convince foreign populations to in some cases worship him as a god. The Egyptians welcomed him as a liberator and crowned him Pharaoh. The Babylonians also welcomed his forces as they resented Persian rule. One thing about Alexander is that yes he inherited the army and original tactics from his father but at the same time he showed an incredible willingness to adapt his tactics. He absorbed Persian horse archers into his army and used them in battle. He adjusted his phalanx including a sort of straddling of his line where he would "deny" his flank to the enemy by holding it back behind the rest of his line and when the enemy on the flank engaged the center he would move in with the flank that held back. This was done as a way to protect the flanks of the phalanx. He was also very resourceful and in my opinion underrated in his sieges which were much more common than pitched battles. At Tyre while the island fortress did prove troublesome for him he and his engineers built a causeway from the mainland to the island from which his army could cross. That causeway still exists to this day. He himself fought in his battles at the head of his companion cavalry and fought bravely and suffered many severe injuries including a stone to his head that temporarily blinded him and definitely concussed him as well as an arrow to his lung. He is credited with one of the first uses of open field artillery when he used artillery to drive some Scythians away from a riverbank so that his men could cross. When he went to India, he and his men abandoned their sarissa since they would be too cumbersome in the jungles, showing another example of adaptation.
As a commander and conqueror he showed the willingness to adapt to enemy tactics, he was able to adopt aspects of the newly conquered peoples' culture to make his rule easier. He was generous with his men and shared the wealth gained from the Persian empire with his men and had their loyalty. He even remembered their names and before battles would come up to them and remind them of their previous exploits throughout the campaign. He was also able through his own personality and ability to command an army of a wide variety of ethnicities.