Why many people say Job
Job is the usual answer when people ask which Bible book was written first. He lives in Uz, outside the later nation of Israel, and he offers sacrifices for his own children as the head of his household (Job 1:1, Job 1:5). That feels similar to the family-centred worship of the patriarchs in Genesis.
Job's wealth is counted in livestock and servants, much like Abraham's wealth (Job 1:3, Genesis 13:2). The book does not mention Israel's kings, the temple, or the law given through Moses. Those clues lead many readers to think Job's story is set in a very early period.
There was a man in the land of Uz, whose name was Job; and that man was perfect and upright, and one that feared God, and eschewed evil.
The oldest story is Genesis
There is a helpful distinction here. Genesis tells the earliest events in the Bible. It opens with God creating the heavens and the earth, then moves through Adam and Eve, the flood, and the lives of Abraham's family (Genesis 1:1, Genesis 2:7, Genesis 6:5-8). No biblical story reaches further back.
But a book can describe ancient events without being the first book written down. Christians have traditionally understood Genesis as one of the books connected with Moses, and Jesus said that Moses wrote of him (John 5:46-47). So Genesis tells the oldest history, even if Job may have an earlier setting or composition.
In the beginning God created the heaven and the earth.
Why the date remains uncertain
Job never identifies its author or gives a date. Scripture gives strong reasons to take its message seriously, but it does not settle every question about when the book took its final written form. Faithful Christians have therefore reached different conclusions.
The book is far more concerned with Job's suffering and his relationship with God than with a timetable. After losing his possessions and children, Job grieves yet continues to turn towards God (Job 1:20-22). Later, God speaks to him, and Job responds with humility and renewed trust (Job 38:1-4, Job 42:1-5, Job 42:6).
A simple answer
The simplest answer is that Job is often regarded as the oldest book in the Bible, but nobody can prove its writing date from Scripture alone. Genesis, meanwhile, contains the oldest events because it begins with creation.
You don't need to solve the dating question before reading either book. Read Genesis to follow the beginning of God's story with the world, and read Job to see that honest grief and hard questions can still belong within faith. Both books invite you to meet the same God.