The region across the Jordan River was once home to a formidable and towering people known as the Rephaim. Overcoming such a massive, powerful nation required nothing short of an open miracle. God actively intervened to wipe out these giants, specifically to give the territory to the Ammonites. This land was granted to them as a reward for their lineage, as they were the descendants of Abraham's nephew, Lot [ביאור יש״ר, ביאור שטיינזלץ]. This act reflects a broader pattern in how God guides the world. He removes mighty nations to pass their lands on to others, just as He did when He handed Mount Seir over to Esau [אבן עזרא].
The process of this conquest followed a very deliberate order. God first entirely destroyed the original inhabitants, and only afterward did the Ammonites take possession of the territory. This complete removal was a practical necessity. The ancient natives, known as the Zamzumim, were deeply cunning and strategic. Even if the Ammonites had somehow gained the upper hand in battle, they would never have been able to live safely alongside such a calculating enemy. Therefore, God had to completely eliminate the threat before the Ammonites could safely settle in their new home [העמק דבר].