I wasn't aware that the Septuagint adds about 650 years in total to the ages of the descendants of Noah through Shem. This would allow about 500 years before the tower of Babel for the population to increase so that there enough people to build the first pyramid in 2450 BC.
Another wee point.
How log do you think it took a sophisticated administration system to evolve? A system which could build hundreds of boats capable of floating massive stone blocks downriver, unloading and transporting them? A system capable of sophisticated agricultural and catering management, breeding livestock, producing beer, bread, vegetables on an industrial scale? decades? Mopre like centuries.
And remember, the first pyramid was not that of the dyn IV king Khufu at Giza; it was that of Netjerikhet Djoser at Saqqara, eigght-odd years erlier - and that undertaking, with its' stone courtyard and buildings, was in many ways more sophisticated thahn the later model.
Even that wasn't the first major undertaking. Sixty years earlier still, in the riegn of Khasekhemwy, a massive structure surrounding his 'mastaba' tomb shows a degree of organisation and sophistication which indicates a very highly developed administration. So that pushes your dates back at least 160 years...assuming of course tyhat the administration in question developed out of thin air, which it manifestly did not.