There have certainly been some discoveries that correspond directly to parts of the biblical text, but most of them have to do with the historical texts like the book(s) of Kings. So, for instance, we have direct archaeological evidence of the kings Hezekiah (referred to directly on Sennacherib’s Prism) and Omri (referred to directly on the Mesha Stele), among others. So if we’re asking if anything in the Bible appears in the archaeological record, the answer is a definite yes. There are also things that we know to be true, like the Babylonian captivity late in the Hebrew Bible: there was a thriving–to the point of rivalling and arguably overtaking the Jerusalem community on a religious level–Jewish community for well over a millennium beyond that.

That being said, much of Biblical Archaeology’s application to the historicity of the Bible itself concludes with an argument for plausibility rather than one for probability. That is, what little archaeological evidence we have for important events in the Bible is scant enough that one is more likely to make an argument that it’s plausible (the conditions might have been right) for this to have happened, than to have the confidence to say that it’s even probable that it happened (let alone definite).

So if we created a spectrum of archaeological reliability that ran Implausible -> Plausible -> Probable -> Definite, Hezekiah and Omri are closer to definite, while something like the story of the Exodus, archaeologically speaking, is closer to the Implausible end of the spectrum, somewhere between Plausible and Implausible.

Speaking of the Exodus, I’ll use that as an example. Someone with little interest in or knowledge of Biblical Archaeology might think that maybe the parting of the Red Sea probably didn’t happen, but obviously there was a large amount of that group of people (Israelites, Hebrews, however you want to call them at that stage) in Egypt and they left and inhabited Canaan.

The truth of the matter is that we don’t even have direct evidence that places that group of people in Egypt at any point, really, but especially at that particular estimated moment in time. What we do have is evidence that some have used to point to it being plausible that they were there. For instance, on a few documents from around Egypt and Levant, there are mentions of a group of people named the Habiru. Some say this corresponds to “Hebrew”, some say it doesn’t, some say it’s actually a term to denote a social class rather than a tribe, some say it has no relation to the topic whatsoever–you get the point. But even if the names on these documents are referring to Hebrews, they show up all across the Eastern Mediterranean in the short span (a few centuries) that the evidence appears, so there’s nothing placing them all (or most) in Egypt.

Other forms of evidence for plausibility include theories (and they are strictly theories; no evidence) that the famous Hyksos dynasties of ancient Egypt were actually the Hebrews.

There’s also zero evidence that a massive group of people (603,000 in the Bible but that’s probably a stylistic exaggeration) spent 40 years living in the Sinai Peninsula. That’s not to say that it’s impossible that that evidence will be found in the future, but you asked about the current state of Biblical Archaeology.

So you might see here the problem with saying that this field “lends credence to the idea that the Bible is completely historically accurate.” It is extremely far from showing that the Bible is completely historically accurate. I think even a hardcore evangelical theologian of biblical inerrancy would find that claim ludicrous (again, we’re talking solely on the basis of Biblical Archaeology–we aren’t talking theology).

Historical parts of the biblical text are easily corroborated, and it’s pretty evident that, macro-politically (the succession of kings, the wars they fought, relations with other nations and empires, like Babylon), that part of the biblical text is fairly accurate. On the level of individual stories, especially miraculous events, there’s virtually nothing from that era, but that’s to be expected. That being said, as I’ve outlined here, there are large parts of the Hebrew Bible (someone can speak more to the New Testament, hopefully) that have virtually zero evidence, and the arguments that people make generally rely on arguments for it having been plausible that it could have happened. This is basically everything prior to the time of the Judges.

Again, that’s not to say that it’s impossible that all these things will be found. I’m not saying this lack of evidence invalidates the text. But we’re talking about the current state of archaeology.

If we’re talking about archaeology of the biblical canon itself (is the Bible we have today the Bible we had back then?), you can find my answer on the Dead Sea Scrolls and why they’re significant here.

For useful texts that were used here, check out:

John J. Collins, A Short Introduction to the Hebrew Bible

Several by Israel Finkelstein

K. L. Noll, Canaan and Israel in Antiquity

Hope this helps!

/u/weinerdog73's response is very good, and I'll try to avoid overlapping with it too much. The one thing I will add is that definitions of "really happened" can vary quite a bit. For instance, I am mostly persuaded from the available evidence that the original worhshippers of YHWH do have a southern origin. The Levites often have Egyptian names, and seem to have retained these names after losing touch with the Egyptian language, leading to false etymology (Biblical literalists take note: it is the very inaccuracy of a detail that suggests there might be truth to the overall narrative). What's more, the Midianite and Kenite hypotheses (worthy of their own posts if I haven't addressed it somewhere else already) suggests that someone brought the worship of YHWH to Israel from the south. The Levites have no land, and only subsist as religious functionaries. Originally they seem to have supervised local shrines to YHWH. The Kenites are likewise wanderers, and seem to make their living as smiths (a rare and valuable skill in those times).

Plenty of Biblical scholars would agree with me, others would not. But let's take that story as outlined as a given for a moment. If there were back and forth migrations of midianite/kenite peoples to and from Egypt, and some of them ended up in Canaan, can we say that "the exodus happened?" Or could we even say "the exodus didn't happen." Neither statement really makes sense. The wholesale departure of a discrete ethnic group numbering hundreds of thousands is quite certainly not historical. But something might have happened, its back-and-forth character captured in the back-and-forth of the narrative (Abraham, Joseph's brothers, and even Moses himself are always going to and from Egypt).

And if there really was a Midianite cultural influence that was transferred by Egyptian migrant laborers to Canaan where it mixed with local traditions and those brought in from Syria and Mesopotamia... well, we might find ourselves agreeing with large parts of the overall narrative in our texts where an Egyptian migrant marries a Midianite and brings her priestly father into his tribe, then eventually his people settle in a land occupied by those who claim a "wandering Aramean" and a "man of Ur" as their ancestors. And all that without accepting a single "historical" claim about Moses, Zipporah, Abraham, or any other figure in the Bible.

Asking if the Bible is "completely historically accurate" is ultimately the wrong question, unreasonably imposing our modernist scientific ways of understanding the world on a time and place that did not think in such terms. Remember the Bible regularly tells multiple stories about the "same" event (Creation, Noah, the departure of Hagar, the Red Sea, Saul meeting David), without really being concerned about the contradictions. History as we know it is a later innovation, and one we still escape on a regular basis to write historical fiction (what could have happened behind the scenes) counterfactuals (what could have happened if things had gone differently), and fantasy (stories vaguely set in our past but often with radical and unexplained alterations to history, geography, and even scientific laws).