Ancient army numbers

[Gaius Julius Caesar]

I wonder.
The Persian empire was vast, had excellent roads, an efficient communication system, well organised goverment of it's provinces. It could draw on manpower from the heart of civilisation, and was able to cross the Hellespont on a pontoon bridge.
But it couldn't organise, mobilise, equip and supply a vast Army?
They dug a canal across the Halkidikki peneinsular to avoid a storm...
Surely, they were an advanced society, and were capable of planning a campaign which relied on both supplies, and requisitioned supply from the lands it crossed?
The Balkans were surely not totally un-cultivated and barren.?
Anatolia was considered a ripe fruit by the Greeks...full of untold bounty.
i think the vastness of the account of the Greeks to describe this would have been inclusive of the vast supply train.