Apart from proposing that there are gaps in the biblical genealogies, which wouldn't be true to the bible, the most logical approach would be to respect the most recent 'fixed dates and' compress early Egyptian dynasties by considering some pharaohs to have co-reigned or just been repeated.

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Compression of the later dynasties was an idea put forward by David Rohl in his book 'A Test of Time'. Like a similar proponent, christian David Downs, they cannot fit king Solomon with the Iron Age IB period, a period where there seems to be poverty in archaeological finds (before recent discoveries). David Downs has practical insight into the reliability of carbon dating that is worth listening to [10]. In effect they would have the New Kingdom and the Early Iron Age pushed later so that Solomon would appear when there is evidence of splendour and well built cities, in the Late Bronze Age.

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Israel Finkelstein, is among other archaeologists who take a biblical minimalism view. He attributes some features of the currently associated with the time of king Solomon with the later endeavours of king Omri. He see ideas of a united monarchy coming embellished from the minds of 7th BCE authors.[12]. However, this view is being overturned. Yosef Garfinkel and Madeleine Mumcuoglu show that the features of the Temple of Solomon as described 1 Kings is evidenced by comparative new finds uncovered at Khirbet Qeiyafa and Motza for the 10th century BCE.[13]. Further indirect evidence of King Solomon is coming to light: Eilat Mazar's excavation of what appears to be the defensive wall that Solomon built  in Jerusalem [16] and extensive copper mines in the south that have been re-dated to the time of Solomon. [17]

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Keeping in line with the fixed dates, we have the view of Amihai Mazar. What may be needed is a balanced view of the expanse of Solomon's kingdom. Yes, we can consider it grand, but we need to realise that it was a hill top kingdom - it ruled from the heights [11]. The cities of refuge given accompanied by pasturelands (1 Chronicles 6:57,67) were strategic centres of defense under David [18]. Solomon, also applied heavy taxes, which could have contributed to the poor archaeological finds, together with the fact that the valuable items of the royals would have been eventually ransacked. 

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Settling on the alignment that chooses the Masoretic Text as the most reliable source of chronology [1] together with the current 'Fixed Dates' of conventional Egyptian chronology (but a compression of the early Egyptian dynasties). Thutmoses III is the candidate for the pharaoh of the Exodus 480 years before the dedication of Solomon's temple. Steve Rudd gives excellent reasons for placing Thutmoses III as the pharaoh of the Exodus in 1446 BC and why he didn't die along with his army when the waters swept in at the Red Sea crossing [14] (though I have dated the Patriarchs Abraham, Isaac and Jacob differently).

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With this alignment we then have the prospect of the pyramids being built a little time after the Flood, which agrees with the fact that Pyramids of Giza did not see great flood damage, In the time of the pharaoh Menkaure, who built the last and smallest of the three pyramids, we do see repeated local flooding that affected the administrative town below the plateau [15]. It's a bit of mystery why the town was built where it was - may be it was related to their ethos in regard to the purpose of the building the pyramid and the afterlife, with the pharaoh always needing to be placed higher. Indeed putting themselves in positions of power, they raised themselves up as gods controlling the regular inundations of the Nile, channeling the nutrients to irrigate the fields. This at a time when the Sumerians moved to higher ground because of the increased salinity of the soil and arid conditions [19]. It is easy to imagine Abraham living during these times when the king of Elam among other kings was looting in Genesis 14. 

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Back to the biblical account: after the Flood we see Noah and his family being blessed.