Thank you for the question on ancient writings, “Is there a story/book older than the Bible?”
As one may know that the earliest surviving book/ codes is Codex Sinaiticus. Codex Sinaiticus is dated to about 325 CE. The Dead Sea Scrolls are dated between first century BCE and into the first century CE.
The oldest surviving written story is the Epic of Gilgamesh, dating to 2100 BCE which is written in tablets, while archaeologists have discovered Egyptian that has hieroglyphs writing dating as far back as 3400 BCE on bones and pottery vessels.
The Israelites didn’t become a nation until Moses as the Israelites were a nomadic tribe living in Canaan. According to the Genesis account, Abram left the Mesopotamian culture, lived in the Canaanite culture, and even ventured into the Egyptian culture. Thus it would be reasonable that those earlier culture would have left some form of writing, drawing or inscriptions of their culture.
Göbekli Tepe is “a Neolithic archaeological site near the city of Şanlıurfa in Southeastern Anatolia, Turkey. Dated to the Pre-Pottery Neolithic, between c. 9500 and 8000 BCE, the site comprises a number of large circular structures supported by massive stone pillars – the world’s oldest known megaliths. Many of these pillars are richly decorated with abstract anthropomorphic details, clothing, and reliefs of wild animals, providing archaeologists a rare insights into prehistoric religion and the particular iconography of the period.”
https://en.wikipedia.org/wiki/G%C3%B6bekli_Tepe
They have found sketched into the megaliths of animals, but no written language as of yet. Verbal transmission became written transmission as society developed where by rulers wanted to record their deeds or history that was verbalized to them. Thus it would be expected to find older writings than the Bible.
SUMMARY: The established cultures from the time of Noah would have left sketching or later writings of their cultural history or laws that would be older than the compiled Bible about 325 CE.
For further perspectives:
https://www.quora.com/Is-there-a-story-book-older-than-the-Bible