Sarah's half-brother King Tushratta of Mitanni invaded Egyptian Syria. On this, Amenhotep III expelled Sarah from Egypt, including Abraham's clan from the Negev.1,2:215,3:52
But to thwart the further advance of Tushratta, Amenhotep III granted Canaan to Sarah,4,5
such that if Tushratta wanted it, he'd have to steal it from his half-sister, thereby making enemies of both Egypt and his family back in Mitanni. To secure the grant for their family, Sarah had to produce an heir. So Abraham and Sarah got married, and had a son who they named Isaac.6
Note that at the time, Canaan was just so many city-states, all reporting directly to the pharaoh, as attested in the Amarna letters. And we hear no mention of anybody like Abraham or Sarah, which questions the historicity of the grant. There was
a position known as the "king of the Retenu" back in Egypt, which seems to have been more of a trade administrator, or tax collector, than a political governor. Perhaps this was the role granted to Abraham. If so, it would explain why he wasn't mentioned in the Amarna letters, being just a civil servant of the pharaoh's, not an authority in his own right. Thereafter we hear that he was a tent dweller,7,8
in a land dominated by competing kings.9
The "kings" would have been the chiefs of the city-states, who Abraham visited.
Amenhotep III commissioned more statues of Resheph, the Canaanite god who protected against the plague, than all other statues combined,10
strongly suggesting that the epidemic began in this time. The plague was blamed on Sarah,11
perhaps to condemn the Hindu prophesy of Abraham, and/or to discredit the Mitannians.
Note that bubonic plague is typically transmitted by fleas. The ancients didn't figure this out, and rather concluded that it was simply spreading through the wind.12
Since Amun was the god of the wind, either he had turned his back on the Egyptians, or was powerless to prevent some other force from usurping his powers to unleash a deadly disease. Either way, there was a loss of confidence in the Amun priesthood. Thus the demotion of Amun, and the promotion of Ra (and later the Aten), were reactions to the general sentiment, not just the unilateral initiatives of the Amarna pharaohs.