I recently met a person who has a master's degree in theology. I took the opportunity to discuss with him about oral or written. He explained to me that God told Moses to write the laws and preserve them for many generations to come. However, the Jewish men had to learn the entire Torah and Talmud to pass along orally to their descendants. The oral ceased after the destruction of the 2nd temple. So the oral transmission was intended to accompany the written at the time Moses received the commandments on Mt. Sinai. Therefore, both existed simultaneously.
Memorization of the entire Torah (or more commonly just the 613 Mitzvot of the Torah) is definitely an ancient Jewish practice. We should talk about the timing of that.
The Israelites of Moses' day installed a system of judges and clan leaders and tribal leaders to administrate justice. Those judges created the 613 Mitzvot (commandments).
The judges among the Jews in David's day definitely were memorizing the Mitzvot. We know because David writes about doing so himself in the Psalms. But they probably weren't doing this to pass down culture or history (the genre of history didn't exist yet), but rather as part of their administration of justice. Today we call this
case law.
The Israelites and Jews apostatized under Solomon and his successors. The Bible tells us that the northern nation (Israel) completely abandoned God in favor of the Baals, until they were eventually destroyed by the Assyrians. Safe to say they weren't memorizing the Law.
In the southern nation (Judah), it gets a bit confusing. All the nobles (aka all the people who could read) were carried away to Babylon in the exile. The Prophets were written around this time, and they demonstrate knowledge of the Law, but... how do I say this? The Prophets don't
endorse the Law. They call for the covenant of the Law to be done away with, in favor of a New Covenant (Jer 31).
Meanwhile, the people left behind in Judah
lost the Book of the Law entirely for two centuries. It was re-discovered during the reign of King Josiah (6th century BC), according to the Bible. At that time, Josiah initiated a reform that brought all of Judah into a strict adherence to the Law. The Law at this time was probably just Deuteronomy, because Exodus didn't exist yet, Leviticus was a separate handbook for priests, and the material that would later become Genesis was a bunch of diverse scrolls that hadn't been combined and chronologically ordered yet.
A century later, the exiles in Babylon and Persia would return to the Holy Land, rebuild the temple, and canonize the Pentateuch into something resembling what we see today.
So, short-story-made-long... the idea that the Oral Law was handed down from Moses until New Testament times isn't true. There wasn't an unbroken chain of people during that time. The entire thing was lost for two centuries!
The practice of memorizing and transmitting the Law orally probably starts with Ezra, in the 5th century BC, which makes sense because he's the one who put the Pentateuch together.