For instance?
Well let's see where do I start?
There is plenty of evidence for the existence of ancient Jerusalem. Excavations in the City of David, today the village of Silwan, just south of the Old City walls, show that the site has been continuously occupied for some 5,000 years. Closer to David's purported time, excavations directed by the late Prof. Yigal Shiloh, uncovered a monumental 20 metre stepped structure, and dated it to the 12th-10th century bce. This could have been the foundation of the Jebusite stronghold, captured and subsequently expanded by David.
In addition to the archaeological evidence, Jerusalem appears in several ancient documents, apart from the Bible. The earliest known reference dates to 1900 bce in the so-called "Execration Texts." The names of the enemies of the Egyptian ruler were inscribed on pottery, which was then smashed in the hope of bringing destruction upon them. Jerusalem at that time was apparently an enemy of Egypt, as indicated by letters written on clay tablets found in the ruins of Amarna, the palace of the reforming Pharaoh Akhnetan. In one of them, dating to the 14th century bce, Abdu-Heba, the king of Jerusalem, writes pledging his loyalty to the Egyptian ruler.
Until very recently, there was no evidence outside the Bible for the existence of King David. There are no references to him in Egyptian, Syrian or Assyrian documents of the time, and the many archaeological digs in the City of David failed to turn up so much as a mention of his name. Then, on July 21, 1993, a team of archaeologists led by Prof. Avraham Biran, excavating Tel Dan in the northern Galilee, found a triangular piece of basalt rock, measuring 23 x 36 cm. inscribed in Aramaic. It was subsequently identified as part of a victory pillar erected by the king of Syria and later smashed by an Israelite ruler. The inscription, which dates to the ninth century bce, that is to say, about a century after David was thought to have ruled Israel, includes the words Beit David ("House" or "Dynasty" of David"). It is the first near-contemporaneous reference to David ever found. It is not conclusive; but it does strongly indicate that a king called David established a dynasty in Israel during the relevant period.
Josephus also mentions him also note the following taken from wikipedia
First, the famous Tel Dan Stele provides the only clear extra-Biblical evidence of King David's existence and status as the founder of a Hebrew dynasty. Dated to the period from the mid-9th to mid-8th centuries BC and erected by an Aramean king (probably the king of Damascus) to record a victory over Israel, the text says inter alia: "I killed [Achaz]yahu son of [Joram kin]g of the House of David." (The words and letters within square brackets have been supplied using biblical content.) While the reading has been questioned, it is accepted by a majority of scholars as confirming the existence in the 9th-8th centuries BCE of a line of kings claiming descent from a dynasty founder named David.
A second stele, the Moabite Stone or Mesha Stele, erected by a king of Moab in about 850 BCE, has also been read as containing the phrase "house of David." Because the phrase that is read "house of [D]avid" appears in a place where the stone is partly broken (the square brackets around the first D indicate that the letter is supplied) and for other reasons, this claim is accepted by some scholars but is ignored or rejected by others.
A third possible mention of King David is found in a standing monumental Egyptian inscription of PharaohShoshenq I (called Shishaq in the Bible) that is dated to 924 BCE—only about forty years after David's death as calculated according to the books of Kings and Chronicles. David's name appears to be included within a place-name that appears among other place-names located in the territory later said to belong to the northern kingdom of Israel and the southern kingdom of Judah. This particular place-name is Hadabiyat-Dawit, translated by Egyptologist Kenneth Kitchen as "highland of David" or "heights of David," and it is located in the Negev region, where the Bible says that David hid as a fugitive from Saul for lengthy periods of time. Kitchen proposed the identification of the biblical David in this inscriptional place-name in 1997. [26]
In 2005, Israeli archaeologist Eilat Mazar, excavating in the most ancient portion of Jerusalem, which is called the City of David, in East Jerusalem uncovered an alleged King David's Palace site, but there is no reliable archaeological assessment currently available.
The strongest argument for the historicity of King David is the area of specific agreement between the Bible and the Tel Dan stele. The biblical books of Samuel, Kings, and Chronicles, all of which are received texts handed down by tradition over the course of some 2,000 years, possibly up to several centuries more, do have some points of agreement with the Tel Dan stele, which was carved in stone during the 9th or 8th centuries BC and then excavated in fragmentary form during 1993 and 1994. The biblical content presents David as a Hebrew king who founded a dynasty called "the house of David" (in Isaiah 7:13, etc.) that lasted more than four centuries. The Tel Dan stele presents David as a king, most likely a Hebrew, and the founder of a dynasty called "the house of David." At the time the stele was carved, this dynasty had thus far lasted approximately one or two centuries.
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