How did Saul become publicly recognized as king after his victory over the Ammonites?

According to the biblical account in 1 Samuel, Saul’s public recognition as king followed his heroic military success in delivering the town of Jabesh-Gilead from oppression by the Ammonites.1

This victory demonstrated Saul's leadership abilities, mirroring the way the charismatic judges of Israel were traditionally chosen through displays of military courage. Following this triumph, Saul was acclaimed as king during a public ceremony held at Gilgal. While other traditions suggest he was chosen by lot or through a private anointing by Samuel, the account of the Ammonite campaign serves as the narrative basis for his public validation and acceptance by the people of Israel.123