At Gibeon, God appears to Solomon in a dream and makes an open offer: "Ask what I shall give thee" (1 Kings 3:5). Watch what Solomon doesn't ask for before you notice what he does. No long life, no riches, no victory over his enemies — the three things almost any ancient king in his position would have requested first. Instead: "give therefore thy servant an understanding heart to judge thy people, that I may discern between good and bad: for who is able to judge this thy so great a people?" (1 Kings 3:9). Notice the self-awareness in that question. Solomon isn't asking to be impressive. He's asking to be adequate to a task he's honest enough to admit is beyond him as he currently is. God's response is worth sitting with: because he asked for wisdom and not long life or riches or the lives of his enemies, God gives him wisdom unmatched by anyone before or after him — and then adds riches and honor on top, unasked, "and I have also given thee that which thou hast not asked" (1 Kings 3:13). The gift you don't grasp for turns out to come bundled with the gifts you didn't ask for either.
The very next scene puts that wisdom to work in public, and it's worth reading as a piece with the dream rather than a separate story: two women claim the same living infant, and Solomon, with no witnesses and no evidence, orders the baby cut in two so each can have half. The real mother's love exposes itself instantly — she'd rather lose her son to the other woman than see him killed — and Solomon gives the child to her (1 Kings 3:16–28). The whole nation, the text says, "feared the king: for they saw that the wisdom of God was in him" (1 Kings 3:28). That's the wisdom Gibeon promised, already doing exactly what it was given for.