How did Alexander the great establish the world's largest empire at the time?

Alexander the Great was famous for his military power and is a legendary figure in history.
Much of what we know about Alexander the Great is unreliable and steeped in myth; a lot of these mythologies were used by Alexander’s successors.
In the Kingdom of Thrace, during the reign of Lysimachus—a successor of Alexander the Great who lived from 361 BCE to 281 BCE—an interesting coin was issued. This coin, which featured the head of Alexander the Great with ram’s horns on either side of his crown, was issued in the ancient city of Parium, in the northwestern region of modern-day Turkey. The horns were the symbol of the Egyptian god Amun—or Zeus, who is often conflated with Amun—from whom Alexander claimed descent. Flanked with these godlike horns, Alexander attained the status of a deity.
Silver coin; left, front,, head of Alexander the Great wearing the horns of Zeus Ammon; right, back, seated Athena.
Silver coin; left, front,, head of Alexander the Great wearing the horns of Zeus Ammon; right, back, seated Athena.
Silver coin; left, front,, head of Alexander the Great wearing the horns of Zeus Ammon; right, back, seated Athena. Image credit: British Museum
Surprisingly, Alexander himself did not issue coins with his own image; his successors did. Why would his successors refer back to their deceased predecessor as they established new empires? The reason is that Alexander the Great was—and still is—a powerful symbol of power, military genius, and conquest, whether or not this description of him is historically accurate. His image, name, and legendary power remained resonant—and politically visible—long after his death.