This pyramid building civilization has many similarities to both the ancient Egyptian civilization and also to the civilizations of Mesopotamia (which you probably mean with Persian-like). From those two the latter is/are actually a bit older and marks the beginning of city building. But nevertheless such large buildings as the Egytian pyramids or the Mesopotamian ziggurats didn't emerge before about 3,000 BC (neither did they in other parts of the world, like America) and in the time of the movie people were still wandering around in small tribes, much more like D'leh's tribe and all those he encounters on his way.
So I think this civilization is rather made-up by Roland Emmerich, though surely influenced by the ancient Egytian civilization (that already influenced his Stargate) and maybe a bit of the ancient Mesopotamian civilizations. But in this time it is an utter anachronism. Emmerich somehow used the fact that the records of this time are rather scarce as a possibility to be a bit creative.
It is actually hinted in the movie that this civilization is connected to Atlantis (which we all know was a civilization that was way ahead of time ;)), when it says that The Almighty and his followers come from a realm sunken into the seas and later when you shortly see a map that has a large island next to africa.
So in fact it has a strong link to a civilization that is rumoured (not by serious scientists however) to have existed in that time, but not to a real proved civilization at that time, though strongly influenced by later existing civilizations. And D'leh's tribe and all the other rather primitive tribes are a more accurate depiction of the civilizations at this time.
EDIT: As a side note, the ending of the movie can be seen as a more or less accurate allusion to the development of civilizations during that time: When the tribe D'leh met during his adventure gives him a bunch of seeds to thank him, D'leh's tribe starts planting crops intead of (or in addition to) hunting. And it was indeed around 10,000 BC (though varying by region) when nomadism was replaced by agriculture, which of course formed the prerequisits for permanent settlement (and thus modern civilizations).
In conjunction with the harder and harder gathering of food and the tribe's starving depicted at the beginning of the movie this provides a general look at the overall civilizational development and its reasons during this time period and gives the movie a somehow historically accurate main theme, with D'leh's particular adventure being just an anachronistic interlude for the sake of entertainment.