It is important to bear in mind that a lot of the techniques that science (specifically, archeology) uses to derive information about ancient cultures and religions can't be validly applied to Judaism. Consider, for example:
One source of such information is the arts, such as statuary, vase paintings, and the like. The Torah outlaws the making or possession of images "of anything in the heavens above, on the earth below, or in the waters below the earth" (Ex. 20:4), "the form of a male or female... of any animal on the earth... of any winged bird... of anything that crawls on the earth... of any fish in the waters below the earth" (Deut. 4:16-18). Furthermore, unlike other deities, G-d is not representable in any form. So that's out; any such image would in fact be prima facie evidence of failure to observe Jewish law properly.
Another is the remains of cultic centers, be they private shrines in people's houses, or major ones funded by the state. In Jewish law, except for brief periods, only one central place of sacrificial worship was permitted (it moved around until it was established on the Temple Mount in Jerusalem, not exactly an area conducive to archeological study). Again, then, any altar or whatnot that you'd find elsewhere would almost certainly have been set up in violation of the law.
Then there is written material, such as monumental inscriptions by various kings in which they mention the gods they worshipped, or copies (on clay tablets or the like) of famous myths that formed part of the basis of the local religion. We Jews have only one written Law, and the rules for writing it are fairly strict - it is to be written with ink on parchment (as indeed is done to this day), a material which generally doesn't survive without efforts at preservation.
So the available scientific data about early Judaism is pretty fragmentary; your average secular writer's description of it is likely to be about 1% fact and 99% conjecture - much of that based on Comparative Religion 101 (and, as above, much of that can't correctly be applied from the outset).
With that said, to the best of my knowledge the earliest known extant part of the Bible is a small silver scroll containing the Priestly Blessing (Num. 6:24-26), found in an archeological dig near Jerusalem and dated to the late First Temple period (about 600 BCE). More complete texts, differing from ours only in detail, are the Dead Sea Scrolls, usually dated to around the 1st century BCE or the 1st century CE.
It is also worth noting, though, that the Samaritans have an independent tradition of the Torah (and of Judaism, although that's not the term they use since they don't trace their descent to the tribe of Judah). Their text of the Five Books of Moses differs from ours but is still recognizably the same, and they also have a book of Joshua whose contents are considerably different - but no others. Now, the Samaritans and the mainstream Jews have been enemies at least since the 5th century BCE, meaning that there is no time since then when one could have borrowed from the other; that, then, is a latest possible date (terminus ad quem) for the writing of the Torah. In a couple of his books, R. Avigdor Miller goes further and points out the following:
The Samaritans themselves claim to be descended from the original Israelite inhabitants of northern Israel. The biblical account (II Kings 17:24ff) states that they are descended from foreigners imported into the land by Sennacherib after he had destroyed the northern Israelite state and exiled its people, but who learned the Torah from Israelite priests whom Sennacherib brought back at their request. Either way, then, the Samaritan scriptures must derive from earlier Israelite originals.
The Israelite and Judean kingdoms were at loggerheads, politically and religiously, almost continuously. In particular, each side considered the other's form of divine worship to be illegitimate. There is therefore no real possibility of either one having borrowed religious concepts from each other; if they both had Torahs that are recognizably the same, they must go back to a common source predating their split - which brings us back to the 9th or 10th century BCE.
Aside from the Pentateuch and Joshua, there are a couple of other biblical books (including Judges, Samuel and Ruth) that describe events before the split of the two kingdoms. But we see that the Samaritans don't have any version of those, which would imply that neither did the northern Israelite kingdom. The reason, R. Miller writes, can only be that those had been written fairly recently, and the Israelite kingdom could feel free to discard them (the more so since many of them are associated with the Davidic dynasty against which they had revolted); but evidently the first six books of the Bible were so old and venerated by that time that they were kept. Which fits well with our tradition, that these books were first written down in the 13th century BCE.