Plucked from the obscurity of the tribe of Benjamin, Saul had only to obey God. There was no amount of sacrifices or anything else Saul could have done to force God’s hand. It looks like it was an act of grace that Saul never really understood.
1 Samuel 15:17 Although you may think little of yourself, are you not the leader of the tribes of Israel? The Lord has anointed you king of Israel.
All Saul had to do was obey God:
1 Samuel 15:22-23 … What is more pleasing to the Lord:
your burnt offerings and sacrifices or your obedience to his voice?
Listen! Obedience is better than sacrifice,
and submission is better than offering the fat of rams.
Rebellion is as sinful as witchcraft,
and stubbornness as bad as worshiping idols.
Unfortunately, he didn’t quite manage it, with the terrible result:
1 Samuel 15:23 So because you have rejected the command of the Lord, he has rejected you as king