That is actually a pretty vague and speculative "proof".
No known archeological evidence available to a group of modern experts?
8th century BC was a long time ago and ANY writings found from that time are very rare and precious.
We have entire libraries of writings dating back to 2,300BC. We have entire libraries of hundreds of thousands of all kinds of writings dating from 800 BC just not in literary Hebrew. We have extensive "letters" from the petty kings of Canaanite "cities" dating from about 1,400 BC written to the Egyptian Pharaoh complaining about other Canaanite groups, outlaws and competitions. These are known as the Amarna letters. They are written in Akkadian cuneiform as Hebrew was not a written language by then.
Textural experts see archaic spellings and letter types indicating there is reason to believe that by 800 BC literary writing was a possibility. This was about 200 years after the life and times of important characters. The Kings, Prophets and Judges that lived before the invention of literary writing include:
Patriarchs & Leaders
Abraham, Isaac, Jacob, Moses, Joshua
Kings of Judah - Southern
Saul, David, Solomon, Rehoboam, Abijah, Asa, Jehoshaphat, Jehoram, Ahaziah, Athaliah, Jehoash
Kings of Israel – Northern
Jeroboam I (founder), Nadab, Baasha, Elah, Zimri, Tibni, Omri, Ahab, Ahaziah, Joram, Jehu, Jehoahaz, Jehoash (Joash)
Prophets – North and South
Elijah, Elisha, Amos, Jonah, Hosea, Joel, Isiah & Mica lived on the cusp of literary Hebrew
Judges (saviors)
Othniel, Ehud, Shamgar, Deborah, Gideon, Tola, Jair, Jephthah, Ibzan, Elon, Abdon, Samson, Eli, Samuel, Joel, Abiah, Amariah and Zebadiah, Abimelech