The comments on this question have correctly pointed out that it is possibly unanswerable because of the variety of meanings attributed to the word "Judaism." The question, as well as the encyclopedia sources it cites, seems to equate Judaism with the monotheistic worship of the Jewish people. When the Jews became monotheistic believers in "Judaism" is up for debate, even if you believe in the literal truth of the Bible. (Remember the golden calf?)
The ancient Jews seem to have worshiped several different gods. They were certainly united in a kingdom at several points, and still considered themselves a nation even after their kingdom was captured by the Babylonians, the Persians, and the Romans; however, the meaning of "nation" differed strongly between Jewish communities, as we learn from non-Biblical sources. Eventually all gods were excluded other than Yahweh, who received the sacrifices at the Second Temple. (source: review article) The history of the Jewish people spans thousands of years, going back to Bible narratives like Exodus that take place centuries before what archaeology can confirm, and the quasi-theological question of when "real" monotheism began can't be answered scientifically.
But to most people, in common parlance, Judaism means Rabbinic Judaism, which arose after the destruction of the Second Temple. Even scholars agree that this is the best way to define the term. Philip R. Davies, in his article "Beyond 'Biblical Archaeology'" (in Hjelm and Thompson, eds., Biblical Interpretation Beyond Historicity: Changing Perspectives, vol. 7, Routledge, 2016), gives a summary that justifies this definition through significant methodological background:
Reinhard Kratz has recently pointed out [in Historisches und biblisches Israel (Mohr Siebeck, 2013)] that Wellhausen's distinction
between the religion of "ancient Israel" and the religion of Judaism
remains a fundamentally important insight. . . . the biblical Israels are a product of various Judahite/Judean communities and not the other way around. . . .
The religion of Judaism – which can intelligibly be dated only to the
second century CE at the earliest – is much more a product of the
scriptures and the "Israels" , depicted in those scriptures, than it is the outcome of any events that occurred in the Iron Age.
Davies does acknowledge that Abraham and Moses lie at the "beginning" of Jewish religion, but the religion itself is much better defined, at least for outsider scholarly purposes, by the image of them in Scripture centuries later than by whatever was going on in Iron Age Israel. There is no such thing as a search for the "historical Abraham" by modern scholars, because it's no longer considered relevant who Abraham might have been outside of Scripture.
This answer may be confusing, but hopefully it can shed a bit of light on why the Dead Sea Scrolls are so important for Biblical scholars. The Jewish people were still in the process of defining their beliefs over the period of 400 BCE-300 CE when the Dead Sea Scrolls were written, and they had not yet consolidated around the styles of transmission, interpretation, authority, reading, and practice that developed into modern Judaism. Yet there is plenty in the Scrolls that seems almost monotheistic and quite familiar.
Short answer: The Jewish people have existed for thousands of years, but the term "Judaism" before the rabbinical era (meaning the late Roman Empire) is basically not useful.