Thousands of years
Due to the De-canonization in 2014, a lot of the details of the Star Wars universe have been "lost". As such, we no longer have specific dates for things anymore. However, several statements littered across the movies and shows incline me to believe that at the fall of the Galactic Republic, recorded history spanned back at least 20,000 - 25,000 years.
The Galactic Republic was founded circa 1000 BBY
"I will not like this Republic, that has stood for over a thousand
years, be split in two." - Palpatine
Episode 2: Attack of the Clones
There was a Republic before the Galactic Republic
"This lightsaber was stolen from Your Jedi temple by my Ancestors
during the fall of the Old Republic." - Pre Vizsla
Star Wars: The Clone Wars - The Mandalore Plot
This Old Republic stood for roughly 20,000-25,000 years
"For over a thousand generations the Jedi Knights were the guardians of
peace and justice in the Old Republic." - Obi Wan "Ben" Kenobi
Episode 4: A New Hope
Even if Kenobi was referring to both Republics combined, 1000 generations is a very long time. We know the Library in the Jedi Temple on Coruscant was exhaustive, so I don't doubt that Kenobi knew this figure for a fact. And if the Jedi kept good enough records to have a count of the generations that passed through, we can safely say that "recorded history" and remembered history spanned roughly 25,000 years.
In addition to the above, we hear of a few events happening "thousands of years ago" with no clear indication of when exactly that was. For example on Malachor:
Ahsoka: This was a battlefield.
Ezra: What happened here?
Ahsoka: It looks like at one time, thousands of years ago, Jedi knights attacked the temple.
Star Wars Rebels: Twilight of the Apprentice: Part I
To answer your question, recorded history spanned thousands of years. As Disney-canon gets more fleshed out, I would not be surprised if we got a more specific date at some point, but for now, we can be sure that the Republic remembered its original founding, and history was recorded from that point forward.
Bear in mind that I answered from the point of view of the Galactic Republic. I would not be surprised if, under the Galactic Empire, historical records were destroyed beyond recovery.