Hello there! You may be interested in a somewhat related post I wrote up three months ago (link here).

A few points: the Bible is our main source for Solomon's reign, and there are no external sources I know of that directly corroborate or disprove our available information. However, fragments of Tyrian records do refer to correspondence between Solomon and Hiram of Tyre. This apparently involved a contest of riddles, which ended with Solomon surrendering large sums of money to the Tyrians. One could take it as a jab at Solomon's supposed wisdom. I should also point out that, according the Bible itself, Solomon's "wise" leadership resulted in Israel's secession from Judah. Assuming that the Book of Kings does present some accurate information about Solomon's reign (and not everyone thinks that's the case), it seems quite possible that Solomon's reliance upon forced labor to build the Temple in Jerusalem alienated the northern population.

K. A. Kitchen, an accomplished Egyptologist with some very conservative views toward Old Testament history, has also made an interesting case for the historicity of the Queen of Sheba and her visit with Solomon, which he interprets as a trade mission. He points out that, prior to the seventh century B.C., royal women were actively involved in day-to-day affairs in various Arabian kingdoms. "After 690, never again do we find any Arabian queen playing any active role whatsoever in history [his emphasis]... There was no rational reason for inventing a story about a queen (rather than a king) visiting Solomon at any time after 650 at the latest..." Kitchen nevertheless acknowledges that there's no additional evidence as of yet for the existence of the kingdom of Saba (which is presumably what "Sheba" refers to) before the eighth century, though other Arabian kingdoms are attested.

I can't say much more than that. I hope you find this helpful! :)

See J. Alberto Soggin, "Compulsory Labor under David and Solomon," in Studies in the Period of David and Solomon and Other Essays, ed. Tomoo Ishida (Winona Lake: Eisenbrauns, 1982), 259-67; K. A. Kitchen, On the Reliability of the Old Testament (Grand Rapids: William B. Eerdmans, 2003), 116-21.

Basically, no. There is no contemporary evidence to support even the existence of King Solomon. No extra-biblical documents from the early first millennium BC mention Solomon. The myth of a united empire of David and Solomon that stretched from Egypt to the Euphrates is a literary invention of Jewish writers in the Persian period. (See "The Horns of Moses: Setting the Bible in its Historical Context" by prominent OT scholar Thomas Römer.)

If there is a genuine historical kernel in the local legends that eventually became part of the Jewish scriptures, he would have been a minor king of Judah in the 10th century BCE. Jerusalem was a small, poor highland village during the 10th century — not a resplendent capital city. (See Finkelstein and Silberman, David and Solomon.) Judah was a marginal chiefdom too small to be mentioned in the detailed description of Pharaoh Sheshonq's military campaign in Israel given by the Karnak inscription. (In contrast, I Kings 14 claims that the Pharaoh's campaign was aimed at Jerusalem, and that he seized the treasures of the Jerusalem temple.)

Similarly, the existence of King Hiram of Tyre, who supplied Solomon with cedar wood for his building projects in the Biblical tale, cannot be confirmed as a historical person by any contemporary or later text. (Finkelstein and Silberman, p. 173) There was a Tyrian king by that name in the eighth century, and his name and deeds have probably been used by the biblical writers to make Solomon look more impressive.