The period being discussed is a period in which there was a political vacuum both in Egypt (Ahhenaten had disrupted the state religion by basically firing all the priests except for those of Aten, the sun god, and there was literally turmoil in Egypt) and Babylon. In this vacuum, the lands between Babylon and Egypt could have a certain degree of autonomy. It is into this vacuum that the nascent Kingdom of Israel arose a flourished for a time.
The Amarna letters are what survives of the diplomatic archive of Amenhotep III, and his son Amenhotep IV, better known as Akhenaten. Hatshepsut (one of the predecessors during the 18th Dynasty) refers in her account of her trip to Punt to an official from the time of Solomon, successor to David. The term "Habiru" ("Apiru") doesn't refer to the Hebrews. Some recent authors have tried to make the early Kingdom synchronize with the Amarna period; the conventional pseudochronology doesn't work in any case.