Firstly, because ‘age’ of ‘civilisation’ alone, already not very well defined, isn’t a great predictor of modern population.

When you say ‘Greece is 3000~ years old’ you’re speaking about a particular cultural identity (which in fact in the sense of speakers of Greek was maybe closer to 4000 years old, though they did not use that name).

But it’s not like these cultures all started with the same number of people at the start: in the examples you give, there were different numbers of Indo-European ‘invaders’ of Greece, Italy and Iran, and they largely absorbed populations already there.

It’s also not true that we should even count them just from when they entered the written record - I’m not sure why we’d expect them to have been the same size then!

If we look at population density today, Greece is in fact more densely populated than Iran (80 people per sq km vs 50 people per sq km). But it has a much tinier area. We may as well ask, ‘But the small island of Naxos entered the written record before the entirety of the United States did, how can it have a smaller population?’ Well, it has a much smaller carrying capacity. You can’t sustain the same number of people in a region of that size.

In fact, populations didn’t explode much from the Classical era until the (modern) Agricultural and Industrial Revolutions which reached those regions in the 19th century, when the carrying capacity of land massively increased, since far more people could be fed, and sanitation and modern healthcare meant fewer people died young. Between industrialisation and the advent of modern family planning in a region, populations have tended to increase massively across the board.

Italy has about 2.5 times the population density of Greece, for a couple of reasons: 1. Though the Appenines and Alps form a large chunk of the country, the country has a higher proportion of flat, arable land than Greece: about 40% of Italy is classified as ‘mountainous’ while Greece is about 80% ‘mountainous’. This leaves 60% and 20% non-mountainous, respectively 2. For a whole complex of debated reasons, since the Renaissance, Italy has been more developed technologically than Greece (which was under Ottoman rule from that time until their 1821-1830 war of independence), which led to its being industrialised earlier, and it is still wealthier today.

That’s density. But Italy also has more than double the area.

Little of the above applies to Iran, which is still more poorly developed, industrialised even later, and is largely dry with large swathes of desert and mountainous terrain. But Iran has over twelve times the area!

It’s entirely expected that Italy and Iran would have a vastly larger population than Greece.