Abstract from Kingdom of Priest - A History of Old Testament Israel by Eugene H. Merill p. 243

An Introduction to a Davidic Chronology

...First of all, though Solomon's age at his accession to the throne cannot be ascertained, he was obviously quite young. In his prayer at Gibeon he calls himself "a little child"; even allowing for hyperbole, this must preclude an age much over twenty (1 Kings 3:7)." Moreover, when David was making plans for construction of the temple, he had referred to his son as "young and inexperienced" (1 Chron. 22:5; 29:1). If Solomon was no more than twenty when he acceded to the throne, he could hardly have been more than eighteen when David discussed the temple construction with him (1 Chron. 22:6-16; d. 23:1). Solomon would then have been born no earlier than 991, thirteen years after David had taken Jerusalem" Solomon's birth followed David's adulterous relationship with Bathsheba by a year or two. That in turn occurred at the time Joab was leading Israel's armies into battle with the Ammonites at Rabbah. A date for this campaign of around 993 is quite reasonable...