Named for a local Bedouin tribe, the Tel El-Amarna tablets (which can now be found mostly in the Berlin and British Museums) were mostly the official correspondence between Pharaoh Amenhotep IV - Akhenaten - and his governors and vassals from places such as Canaan, Syria, Babylonia, etc. They date mostly from around 1380 BCE and were written in Akkadian, the language of diplomacy of the era... Now, guess what repeatedly comes out in this official correspondence between Pharaoh and his vassals in Canaan and the surrounding areas? Complaints about invasions of the Habiru, the Hebrews. While some scholars debate the details, most agree that the time - with even newer confirmations by excavations in Jericho - fits into the period of Joshua's conquests of Canaan. Like many other accounts in the Hebrew Bible, we indeed have good supporting evidence from elsewhere to support the Jews' own version of these events. And what makes it even better is that this often comes from those viewing the events from the "other side" of the picture. This is no small point. Corroboration is very important to any serious scholar. Not many religious texts can match the corroboration found for those of the Jews.This topic, for obvious reasons.
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.