While in the desert, the Israelites picked a fight with the Canaanite king of Arad who lived in the Negev desert
(Numbers 21:1-3)

That would be surprising, since Arad was only founded several hundreds of years later. Several other biblical Negev desert cities indeed existed - but had been abandoned for centuries when the Israelites arrived.

The anecdote in the bible raises plenty of questions as it is:

When the Canaanite king of Arad, who lived in the Negev, heard that Israel was coming along the road to Atharim, he attacked the Israelites and captured some of them. Then Israel made this vow to the LORD : "If you will deliver these people into our hands, we will totally destroy their cities."  The LORD listened to Israel's plea and gave the Canaanites over to them. They completely destroyed them and their towns; so the place was named Hormah. (Nm 21:1-3)

Ok, fair enough. But a little later on, we read a completely different version of the same story. In Judges 1, we read how the Israelites first conquer half of Canaan, including Jerusalem, before some of them turned to Hormah:

Then the men of Judah went with the Simeonites their brothers and attacked the Canaanites living in Zephath, and they totally destroyed the city. Therefore it was called Hormah. (Jgs 1:17)

According to bible scholars, this is a clear indication that the bible combines several different Canaanite conquest stories. And obviously, you shouldn’t take them too literally.

Archaeology supports that. Archaeologists have identified and examined several ancient ruins that must have been Arad and Hormah, the two cities mentioned in the bible. Researchers aren’t exactly sure which is which.

But one thing is certain: none of the places was inhabited at the 13th century, the time when the Israelites are believed to have crossed the desert.

‘Hormah’ translates as ‘broken rock’ or ‘destroyed place’. This strongly suggests that the place was destroyed in prehistoric times and that the bible sought to give an explanation for its destruction.

In Joshua, there are plenty more examples like these: the most famous ones are Jericho and Ai, places that were already in ruins as long as people could remember. The bible's answer: that's because Joshua did it! But archaeologists know that this isn't true. The cities had already been destroyed much earlier.

Finkelstein and Silberman: "The bible unearthed" (2003)

William Stiebing: "Out of the desert? Archaeology and the exodus" (1989)