Thank you for the question on the historicity of the Bible, “What proof is there that biblical myths are actually part of the historical record?”
As one ponders this question, it depends on what time frame from which one is asking that question. For example if one was asking that question in the 15th or 16th century, one would question the historicity of the Old Testament. There would be the question of where is the proof of the Assyrians or Babylonians ever existed, the names of Egyptian pharaoh’s mentioned in the Bible or names of ancient rulers.
In our 21st century, no one question the Biblical citation of the Assyrians or Babylonians with its associate rulers as Sennacherib or Nebuchadnezzar. This has been confirmed with archaeological discoveries of cities and cuneiforms. Egyptian records confirm the existence of Egyptian rulers as Rameses or Neco. Most scholars would concede that the Biblical account to the 8th century BCE is true. Dating further back is questioned. Thus the question is this: If the Biblical record is correct in citing the Assyrians and Babylonians, could the record be true on earlier events.
Scholars debate whether there is any evidence of Solomon’s Temple or that the Torah existed before the 6th century. I cite for one’s reading and consideration of the archaeological findings that relates to the Bible in this cite: List of artifacts in biblical archaeology – Wikipedia. Wikepedia is a general good working site. Most recent discovery of the Elah Fortress, dating 1050–910 is the first Hebraic potsherd that mentions slaves, widows, and orphans as well as judge and a king. Most scholar agree that the writing is early Hebrew because of the verbs being used. One can read more on the Elah Fortress on this site: https://mfa.gov.il/MFA/IsraelExperience/History/Pages/king-david%27s-palace-uncovered-in-elah-valley-18-jul-2013.aspx as well as translation of the potsherd.
As one knows digging on the Temple Mount is restricted by the Arabs as archaeologists have limited access to the site. Will there be more evidences to surface? I believe so.
The Flood of Noah has been labeled a fable, but is it? As far as I know every mountain top from Mount Everest to the Andes Mountain even to the Rocky and Appalachian Mountains have seashells on it. This would imply that at one time those mountains were beneath the water. Tectonic shift would only lift up what is on the ocean floor and can it be a coincident that all mountain tops except for volcano have seashell on it. The recent discoveries of “ocean” of water in the crust of the earth gives some credence that there were more water than there is now. For one’s reading see this site: The Hunt for Earth’s Deep Hidden Oceans | Quanta Magazine and others similar to it. It does not prove there was a worldwide flood. It points that there is more water on the earth than what scientist once thought which the Bible states that the water receded into the earth as the landmass rose and the earth’s water burst forth in the Flood and receded back into the earth. Can there be something to the Scriptures description of the earth and its history? That is for one’s contemplation.
The bottom line is what proof/evidence is one looking for in which one may consider that there is something to the Bible and that it is not all just a fable/myth. How far back historically will one accept as being historically accurate that is collaborate by archaeological findings? Do one stop at the 8th century or 10 century BCE?
SUMMARY: The Bible can’t be a mixed of fable and history for the two will collide. It is either all fable or all true.
For more perspectives: