My guess is that improvements in infrastructure and other things made it easier for an empire to be that big without being overstretched.
According to this list of largest emires to date (each was the larges twhich had existed up to them):
List of largest empires - Wikipedia
The Achaemenid Empire Empire reached 3.6 million square kilometers or 4.49 million square miles in 539 BC and it reached 5.5 million square kilometers or 2.12 million square miles in 500 BC.
There were only four later record breaking empires in history.
The Xiongnu Empire reached 9.0 million square kilometers or 3.49 million square miles in 176 BC.
The Umayyad Caliphate reached 11.1 million square kilometers or 4.29 million square miles in AD 720
The Mongol Empire reached 13.5 million square kilometers or 5.21 million square miles in 1227 and 24.0 million square kilometers or 9.27 million square miles in 1309.
The British Empire reached24.5 million square kilometers or 9.46 million square miles in 1880 and 35.5 million square kilometers or 13.71 million square miles in 1309.
Of course there were other empires larger than the Achaemenid Empire after the Xiongnu Empire in 176 BC. But none those empires was larger than the Xiongnu Empire or a new record breaker until the Umaayyad Caliphate in AD 720.
Empires which later exceeded the maximum area of the Achaemenid Empire included the Xiongnu Empire around 176 BC, the Western Han Dynasty around 50 BC, the Eastern Han Dynasty around in AD 100, the First Turkic Khaganate around AD 557, the Rashudin Caliphate in AD 655, the Umayyad caliphate in 720 (the first to be larger than the Xiongnu Empire), the Abbasid Caliphate in 750 (the second to be larger than the Xiongnu Empire), The Mongol Empire in 1270 or 1309 (The third to be larger than the Xiongnu Empire), the Yuan Dynasty in 1310, part of the mongolt (the fourth to be larger than the Xiongnu Empire), and the Golden Horde Khanate in 1310 a part of the Mongol Empire. The other eight empires larger than the Achaemenid Empire were all later gunpowder era and/or colonial empires.
In post number 5 thread starter
Girgisjus saud:
Allow me to rephrase. The widespread use of high carbon steel around 500 AD.
So that leaves only three empires larger than the maximum size of the Achaemendi Empire before AD 500. The Xiongnu Empire around 176 BC, the Western Han Dynasty around 50 BC, and the Eastern Han Dynasty around AD 100, But three exceptions are enough to prove that the initial post makes an inaccurate statement. Adnpossibly Girgisjus later changed the later cut off date.
I see that Girgisjus later changed the latest cut off date to:
Allow me to correct myself, the late 3rd century BC.
The late 3rd century BC was the period from about 351 BC to 301 BC.
It should be obvious why there wasn't a larger Empire than the Achaemenid Empire in the Middle East during the peak of the Achaemenid Empire and the 301 BC. The Achemenid Empire was still ruling most of the Middle East during the beginning of that period, but not as large as it once was. Then most but not all of the Achaemenid Empire was taken over by Alexander III of Macedona. And later most but not all of Alexander's territory was taken over by the Seleucids. So the Middle East became more and more divided, but the largest remaining state was sill far too large for other middle eastern states to rivel the Achemenid Dynasty at iits peak. So that left India, China, and the Asian grasslands as places where large empires might possibly have arisen.