The Chinese not only created a great civilization, but seem to have no trouble succeeding as a minority in other people's nations. The Chinese minority in Indonesia, for example, is a frequent target of hostility because it's so successful.
Likewise, the groups which lag in Western nations tend to lag everywhere. Their own ancestral homelands are impoverished and what little prosperity they have is usually the result of intervention by others (European colonialists, for example).
I'm not quite sure I know what you mean when you ask about cultural factors contributing to IQ in Persia, Greece, etc. Are you arguing that these nations ended up with high cultures because of high IQs, or vice-versa?
That is your argument. Do you think that because of Greece was civilized long before Norway was that you could find a higher IQ average in Greece than in Norway?
IQ is significantly determined by genetics, about 40% according to most studies. That means environmental/cultural factors account for the other 60%.
So if you had the choice of having “average” genetics and being raised as the son of high achieving high IQ parents or having the genetics of those same high IQ people and being raised by an “average” American family you are far better off (20% better off) picking being raised by those parents rather than having their genetics and being raised by average people.