How can there be "no eyewitness accounts to the Exodus or Joshua"? Aren't the books called "Exodus" and "Joshua" purported to be eyewitness accounts?
You are not using your brains here.
If it was eyewitness accounts, then those witnesses would be contemporary to who ever wrote these books. They are not.
We have no evidences whatsoever that the Bronze Age Israelites wrote anything down in the 2nd millennium BCE.
The book of Joshua is one of those books, like Deuteronomy, were written in the time of King Josiah, from the late 7th century BCE, to the time of exile in the 6th century BCE. Although the Deuteronomy is listed under the Torah, it was certainly not written by Moses, unless you believe that Moses could write about his own death.
From Deuteronomy to Joshua, they were written centuries after the events supposedly took place in the Bronze Age, so it can't be eyewitness accounts.
There are no books of Genesis, Exodus (and others that were attributed to Moses), Joshua, Judges or Samuel in the 2nd millennium BCE.
Second.
According to 1 Kings 6:1, when king Solomon had the construction started with the Temple, in the 4th year of his reign, the exodus took place 480 years earlier:
1 Kings 6:1 said:
6 In the four hundred eightieth year after the Israelites came out of the land of Egypt, in the fourth year of Solomon’s reign over Israel, in the month of Ziv, which is the second month, he began to build the house of the Lord.
I did a calculation of the reigns of rulers of two kingdoms, working backward from the Babylonians destroying the Temple in 586 BCE, all the ways to king Solomon. See Timeline of the Israelite kingdoms.
Supposedly, Solomon ruled for 40 years, which means he started about 970 BCE, and that would mean 4th year of his reign in 967 or 966 BCE.
So adding this 480 to about 966 BCE (Temple foundation), which would mean the exodus is dated to about 1446 BCE.
1446 BCE would mean that Moses was born in 1526 BCE and died in 1406 BCE. And 1406 BCE, that would mean Joshua began his invasion shortly afterward.
According to Exodus 1:11, the pharaoh had the Israelite slaves building the cites of Pithom and Rameses in Goshen.
I know for a fact, that neither cities were built at this time (1526 BCE).
Pithom, in Egyptian known as Per-Atum, meaning the "House of Atum", and Atum was a creator and sun god. Per or "house" can refer to an Egyptian city, palace or temple.
In the 19th century, archaeologists found 2 sites, just 8 miles apart, that have the inscriptions "Pr-Itm" (hence, Per-Atum or Pithom) at Tell El Maskhuta and Tell El Retaba.
Evidences showed that was only occupied in 18th to 17th centuries BCE, during the time of the Hyksos occupation of northern Egypt. So that least, a couple of centuries before 1524 BCE.
And as to Rameses in Exodus, that was at least 500 years after Per-Atum. Rameses is known as Pi-Ramesses (House of Rameses), named after 19th dynasty's greatest king - Ramesses II (1279 - 1290 BCE).
So neither cities were built in the date provided in 2 Kings 6:1.
Third.
1406 BCE is not date of any invasion into Canaan.
From 1446 to 1406 BCE, the 40 years wandering, would be paralleled to the time of 18th dynasty of Thutmose III (1479 - 1425 BCE) and his son Amenhotep II (1427 - 1397 BCE). Canaan and Syria were conquered by Thutmose, and Canaan remained his son's control.
So Joshua couldn't have led the invasion after Moses death in 1406 BCE.
Lastly, there are no evidences that the Israelites written anything remotely "Hebrew".
The earliest written language in Hebrew alphabet, is what experts called palaeo-Hebrew alphabet, which flourished between 10th century BCE to 5th century BCE. Although paleo-Hebrew can be seen as late as 2nd century CE, Aramaic alphabet became more popular throughout the Levant, by 5th century BCE.
No scriptures of what you call "Old Testament" in any shape or form exist in the Bronze Age, where Abraham and Moses supposedly flourished in 2nd millennium BCE.
AND, no paleo-Hebrew inscriptions were ever found before the 10th century BCE.
The oldest writings in Hebrew, were inscriptions found on the Zayit Stone and the stone tablet known as the Gezer Calendar, both of them have been dated to the 10th century BCE. None of them related to the bible.
The oldest evidence of the bible, is the badly fragmented Ketef Hinnom amulet, known as the Silver Scroll, dated to 700 BCE, which contained a couple of verses from Numbers.
Judging by all of these points, I doubt very much on historicity of the Exodus and Joshua, since all records and evidences are against the Old Testament, regarding to mass liberation and odyssey, plus invasion.
You only get some parts of the 2 Kings books that match with history and archaeology.
You really don't understand the concepts of eyewitnesses, do you?
If the books were written centuries after the events supposed to take place, then they aren't eyewitness' accounts.