Jew is harder to trace than Hebrew or Israelite. Hebrew is a distinct language in the Northwest Semitic group. It split off of the Canaanite language in the second half of the 2nd Millennium B.C. There has been a lot of attention dedicated to connecting Hebrews with Amorites. Certain Hyksos kings have been connected with early Hebrews because they practiced monotheism . The theories don't exclude each other because some Hyksos were Amorites.
Hebrew speakers or Israelites were at the fringes of civilizations that gave us historical records. The near east in the Middle Bronze Age (1500-–) was an Egyptian territory. Therefore we have accounts of people in Egyptian records who may have later formed the Israelites. There are some tantalizing bits in the Amarna letters. While the Merneptah Stele is accepted as mentioning Israel, connecting earlier groups with it gets highly controversial. Israelites could have been Hyksos that reentered Canaan.
The Kingdom Of Israel emerged during the Bronze Age Collapse. This was a period of chaos that followed the collapse of the Bronze Age empires in the Near East. Sea Peoples from the Mediterranean hammered Asia and Egypt*. It is during this period that the Hebrews who had been problematic to Egyptian rule formed the kingdom of Israel. They were already well established in Canaan and were able to come to the front during this volatile period.
Israelites distinguished themselves by pyrotechnical and metallurgical skills; they led the iron age and premiered in glass making . This makes them fairly unique if they were nomadic. By the Iron Age, Israelites were a distinct group of people in a distinct, very desirable strategic location. They were set out from their neighbors in technological abilities.
Addressing Jews, we can hardly speak of them before 722 B.C. This is when the Northern Kingdom of Israel fell to Sargon II. Southern Israel, or Judah, would have taken on an increased importance now that the North was occupied. Archaeological evidence shows that Judah had no concentrated settlements before this time . At this point though, it rapidly grew. It was likely populated by Israelites escaping from the north. If there was a powerful tribe call Judah before this, we don't know anything about it**. This is the point when Jewish history begins because the Bible is correlated with Assyrian records. The Israelites did have a very particular tribalism, though, with certain marriage customs.
Response to comment, going even further off track:
Israel existed, but that it was united under Judah may be a piece of propaganda. If it is real, then it has been highly embellished in the bible. It's really going against the grain of what we know archaeologically about Judah. It would would be in stark contrast to the contemporary situation in the Near East. Egypt, Assyria and Babylon were all in a near state of Anarchy that didn't end until the 9th century. This is when the united kingdom ended. Could its fortunes have been the exact opposite of the Near East as a whole? It would have experienced some for of prosperity through its groundbreaking Iron trade. That it was involved in the silver trade with Phoenicians is known. There probably was an early iron age kingdom of Israel that is embellished.
Another answer due to changes to question that I didn't see:
I realized that you changed your criteria to anthropology and genetics. Juris Zarins has proposed the most interesting theory of Semitic, or proto-Semitic origins. He says that they were a fusion that occurred in the Negev Desert between Harifian hunter gatherers (microlithic traders) and Pre-Pottery Neolithic B settlers. These people invented Pastoral Nomadism and fanned out across the Arabian Peninsula c. 6500 B.C. They developed into Proto-Semites.
Semitic people comprised their own civilization of sorts. It may be more correct to say that they were present from the very beginnings of civilization. They existed in Lower Egypt during the earliest days of Egypt, and lent it many of its advancements . There was also a Semitic component in Sumeria in the earliest days of Sumer (Kramer, 1963). At this point, they are contrasted with the Sumerians with their agglutinative language, who may be related to the Indic people.
There may have been a Hebrew component in the Early Bronze city of Ebla. The tablets unearthed at Ebla showed Semitic civilization that were proto-Hebrews . There are names like Adamu. There is also the "Genesis Tablet". Syria is probably the real cradle of civilization, not because of agriculture but because of commerce. Syrian civilization at this point was definitely Semitic. It may have been influenced by Sumerian colonists of the Uruk period. It could have been influenced by the preeminent multicultural city of Mari. This is apparent by the "Nabi" prophets that travelled from Mari to distant lands. Unlike the common Mesopotamian diviners and fortune tellers, the Nabi'utum were speaking of a great, singular force . There is also the connection of , -iah or yah with the Sumerian god Ea (Enki).
Lord of heaven and earth:
the earth was not, you created it,
the light of day was not, you created it,
the morning light you had not [yet] made exist.
~ Genesis Tablet
There were two influxes of Semitic people that broadly affected history in the Bronze Age. The second ones, Amorites, are the candidates for the Hebrews. The first were the Akkadians, that had been in Northwest Sumer since time immemorial. They were a settled, agricultural people.
The next were Amorites, who first took over Syria in 2300 B.C. before spreading into Mesopotamia c. 1800. Like Syria, the Levant experienced a complete collapse of urban culture and dominance of nomadic raiders around 2200B.C. These nomads could have been another people like Hurrians (Biblical Horites) . Amorites definitely came to the region in the Middle Bronze period when they also spread to Mesopotamia. This migration may be represented by the Patriarchal stories.
By the Iron Age, Amorites were replaced by the related Aramean people in Syria. Arameans spread throughout the Near East, like the Akkadians and Amorites had. This was the larger picture of Semitic civilization, from which Israelites and others in "Canaan" were distinct.
*The view that Philistines are a Greek 'Sea People' is reinforced by the recent discovery of a Philistine Cemetery in Palestine.
**I think that the Tel Dan Stele is fake
 I read this at Brittanica.com but now I can't find it. There is a similar claim here at citation 10: https://en.wikipedia.org/wiki/Kingdom_of_Judah
 Hamblin, William J., Ancient Warfare in the Near East to 1600 B.C. Routledge, 2006. I don't have it in front of me but it was the chapter on Bronze Age Canaan. The Egyptians played the primary role in the reduction of Canaan c. 2250.