Being awfully broad as it is, it is nevertheless an issue that might be addressable.
But the terminology needs to be clearer. "Jews", in our modern sense, sprang into existence only after 70 CE. Some scholars argue that this process took even longer. Before that we have Israelites, Yehudites, Judeans, Juda(h)ites, Hebrews and so on. Those terms are partly interchangeable and partly quite distinct.
"Genetically and physically distinct" are very disputable terms as both concepts here are on the border of (scientific) racism, and unfortunately a bit too far on the wrong side of that border. "Ethiopian and Oriental Jews" are by far not the only groups that thwart such attempts. The modern day Samaritans, Djerbans and Lemba, to name just a few prominent groups, add a very colourful genetic makeup into the statistic. Such a biostatistic seems to make it easy to construct clearly defined stereotypes – while in reality neither the individual nor the spectrum of people, communities and peoples are well depicted. Israelite origins are to be found in cultural distinctions and separations, not in biological or even pseudo-biological categorisations:
Views about a genetic basis for Jewishness have been both triumphalist and cautionary. Goldstein has written, “Our genetic heritage is ours to treasure, to explore and to marvel at.” However, Entine has warned, “But DNA is certainly a problematical way to establish identity. Despite the understandable excitement that comes with exploring our genetic attic, there is a clear danger in granting far too much explanatory power to the genes… Only genes confer the mystique of indelibility.” Sand has taken an even more negative tone, warning:
Like the field of physical anthropology in the late nineteenth and early twentieth centuries, which released dubious scientific discoveries to a race hungry public, the science of molecular genetics at the end of the twentieth and the beginning of the twentyfirst century feeds fragmentary discoveries and half-truths to the identity-seeking media.[…]
Jewish genetics is unlikely to replace the hegemony of Jewish law and Jewish culture, nor should it. But as population genetics gains a foothold in the community, with Jews and non-Jews alike wanting to know about their origins, ancestors, and relatives, it will take its place in the formation of group identity alongside shared spirituality, shared social values, and a shared cultural legacy.
(Cited from Harry Ostrer: "Legacy: A Genetic History of the Jewish People", Oxford University Press: Oxford, New York, 2012.)
Concentrating on culturally defining aspects we can then say:
Those who wrote and re-wrote the Torah were mainly exilic and post-exilic Israelites, or rather their priestly and royal servants – a small elite – compiling some older stuff from often oral traditions and interweaving a lot of new material to form a belief system and legitimacy for their religious and regal power structures.
The beginning of Israelite ethnogenesis is tied to the great bronze age collapse. Canaanite city states and their political and cultic system, largely under Egyptian control, broke down. Fleeing or emigrating Canaanites from those cities started to settle in the central highlands and joined nomads and pastoralists there, seemingly adopting a much simpler lifestyle, all of them still being clearly the offspring of the previous cultures and ethnicities. When this process came to a stage as definitely recognisable in archaeological remains is debatable, but Finkelstein sees the Omride dynasty as the first point in time where biblical narrative and physical evidence start to match in any way.
That means that this process took from the great collapse already mentioned until the early iron age and first manifests itself in the archaeological record with very sparse settlements and later gave rise to the original state of Israel, the so called Northern Kingdom.
The self consciousness and image of that people is hard to define, since most of what we have as historians is the first part of the Bible. That book heavily distorts the picture and mostly paints an idealistic, programmatic picture, resembling more a vision than a fact. Our texts are portraying strict monotheism, but at the same time they are retaining hints of different, polytheistic people (the normal population, the 'sinners'), matching up the condemnation of idols and heights with a huge number of material finds in terms of statues and figurines of gods and holy places and their markers in stone. In reality the borders and cultures, and the borders of culture where much more in flux and weakly defined.
One of the most prominent features to observe is that while the Philistines in what is now the South of the modern day state of Israel ate really a lot of pork, the Israelites in what is now considered Palestinian territory started to avoid pigs. The most sensible guess here is that this was one of the first identity markers that separated early Israelites from their surroundings in the early iron age.
Debates about the origin of Israel further complicate questions about the distinction between Israel and the other Canaanite groups. The earliest identification of Israel is found in the Merneptah Stele or Israel Stele from the thirteenth century BCE where the determinative references Israel as a people and not a city-state (see also John Huddlestun’s essay in this volume). Questions about Israel’s origins are complicated, however, by larger sociological issues concerning ethnicity and identity. Although there is no consensus about the origins of Israel, one hypothesis maintains that Israelites were originally Canaanites who developed a distinct self-consciousness centered on their religious devotion to Yahweh. Indeed, underlying the statement in Ezekiel 16:3 – “your origin and your birth were in the land of the Canaanites; your father was an Amorite, and your mother a Hittite” – might be a subtle acknowledgment of Israel’s Canaanite and Amorite origin. The Merneptah reliefs at Karnak might lend further support to this view as they depict Israelites with the same clothing and hairstyle as the Canaanites.
Whether one agrees with this hypothesis or not, the Israelites living in the land of Canaan, surrounded by Canaanite culture, and speaking a similar language, were “frequently, and understandably pictured as absorbing customs and beliefs of Canaan…”. These similarities shed further light on the animosity exhibited toward the Canaanites and the Amorites in the biblical text. The biblical writer emphasizes the differences between this group and Israel not only because its constructed history required justification, but also because such differences were fundamental to the formation and maintenance of Israelite identity. If the society, religion, stories and perhaps even the origins of Israel were acknowledged to be similar or related to those of the Canaanites, then the identity of Israel as a special and separate group chosen by Yahweh, an idea essential to Israel’s self-understanding, would be undermined. No wonder that the biblical narrative so frequently juxtaposes Canaanites with Israelites; an Israelite is that which is not Canaanite or Amorite. Hence, the pleas in the text to not worship their gods, to not inter-marry with them, to not follow their behavior and even to eradicate them convey this fear over the loss or weakening of Israelite identity. It is thus surprising that scholars have seen in Canaan an ever-changing cipher for other entities and groups necessary for the reinforcement of Israel’s identity. (From Song-Mi Suzie Park: "Israel in Its Neighboring Context" in: Susan Niditch (Ed): "The Wiley Blackwell Companion to Ancient Israel", Wiley Blackwell: Chichester, 2016.)
Eric H. Cline: "1177. The Year Civilization Collapsed", Princeton University Press: Princeston, Woodstock, 2014.
William G. Dever: "Who Were the Early Israelites and Where Did They Come From?", William B. Eerdmans: Grand Rapids, Cambridge, 2003.
Israel Finkelstein & Neil Asher Silberman: "The Bible Unearthed. Archaeology's New Vision of Ancient Israel and the Origin of Its Sacred Texts", Touchstone: New York, London, 2001.
David B. Goldstein: "Jacob’s Legacy. A Genetic View of Jewish History", Yale University Press: New Haven, London, 2008.