‘ And the children of Israel arose, and went up to Bethel, and sought counsel of God, and they said, “Who should first go up to battle for us against the children of Benjamin?” And the Yahweh said, “Judah shall go up first.”
The forty units moved from Mizpeh to Bethel, a recognised holy place, where the Ark of the Covenant (Judges 20:27) had been brought. Usually it was at Shiloh, in the Tabernacle, but it had been brought to Bethel, probably in preparation for war. (The Tabernacle may have been brought as well, but for fighting it was the Ark that was important.).
Probably it had been brought here because it was the nearest holy place to Gibeah in readiness for the needs of the tribal confederacy during the war. For the Ark was often used to lead into battle (compare Numbers 10:35; Joshua 6:4; Joshua 6:11; 1 Samuel 3:4-7; 1 Samuel 14:18). But it proved not to be efficacious when God was displeased with Israel. It was not intended to be a Talisman but a reminder of the presence of God with them. Thus it was only effective when God was with them.
Bethel was where God had revealed Himself to Jacob/Israel their ancestor (Genesis 28:19-22; Genesis 35:1). And there they sought God's guidance. They were on a sacred mission and looked to God to guide them. This may have been through the Urim and Thummim or by casting lots (see Joshua 18:8-10), the answer to which would be taken as indicating Yahweh's will (Proverbs 16:33). This prevented any feeling of resentment with regard to the matter, otherwise each might have argued for the privilege of leading into battle. And the decision was that the units of Judah should lead into battle.
“Sought counsel of God.” Probably a technical, widely used phrase which would explain why it says ‘God' and not Yahweh.