Because of the historical association of Saul in the 1000s or 900s BC and the destruction of Gibeah at the hands of Shoshenq, it is hard to actually place David or Solomon into the timeline. David is meant to be a contemporary of Saul but this is probably a later invention. In the Septuagint it is Jeroboam who takes on a similar role to that of David in the Saul story. While Saul seemingly had no real relationship with Jerusalem. But if he did maybe he tried to subjugate Judah, with mixed results, and this is actually where the later association with David in the Bible comes from.
But in any case David might not even have been contemporary with Saul. I think Saul probably reigned in the 1000s BC or early 900s BC. Shoshenq invaded Canaan between 940 and 930 BC. Jeroboam was claimed to have become king around 930 BC, this is not likely to be a coincidence. Probably the leader that overthrew Saul's son was not David but Jeroboam. Shoshenq did not attack Judah at that time (although the Bible claims Shishak sacked Jerusalem in the time of Solomon's successor, but this is made up as Shoshenq does not mention it). So David was either a very minor ruler OR there was nothing in Jerusalem worth sacking at the time.
In fact in Shoshenq's own accounts all the towns he mentions are in the north, he does not even mention Jerusalem. Which if a polity in Jerusalem was powerful it not only could have provided much plunder, but also been a good target to take out so as to eliminate the threat. But Shoshenq did not sack Jerusalem, he sacked multiple towns in the north instead, which means he fulfilled both of those things in the north instead.
That doesn't add up if there was a Jerusalem Empire ruling all of Canaan, or some remnant of it in the south. So in 930 BC either David (or his successor) was an extremely minor player, when Shoshenq was destroying the northern kingdom. OR David in Judah (not in Israel as in actuality David has no connection to Israel or the northern kingdom) had not been ruling yet by 930 BC, possibly making it so that David was from the 800s BC instead of the commonly cited 1010 BC to 970 BC numbers given.
There is a good chance that Solomon, Rehoboam, Abijah, and maybe even Asa are made up. Asa is the king of Judah at the start of Omri's reign in Israel. Omri who is attested to historically. But Omri seems to have subjugated Judah, so was David the king of Judah at that time? I don't think so. David then was probably a king in Judah after 930 BC but before the reign of Omri in 880 BC. We don't even really know what he did though other than found the "House of David" in Judah. Maybe he was alive before 930 BC but if he was then he must have been so minor that he was neither a threat to Israel in the north, nor to the Egyptians under Shoshenq.