The idea of Job-as-oldest is based on multiple pieces of evidence, not necessarily all accepted by everybody who believes that Job is the oldest book. Indeed, not all are compatible with each other. In brief, the evidence is:
The authorship is traditionally attributed to Moses. Since the Books of Moses (i.e., the Pentateuch) were edited/compiled/written after Moses, this would make Job the oldest book.
The author is often assumed to be Job himself, and Job is assumed to have lived in Patriarchal times, perhaps a contemporary of Abraham. This is sometimes reconciled with the traditional attribution of the authorship of the book to Moses by assuming that Moses edited the book into the current form.
Job is mentioned in Ezekiel, itself one of the older books of the Bible.
The language of Job is notable different to the rest of the Bible. This is variously interpreted: (a) it means the language is archaic, and Job is a very old book, (b) Job is based on an Aramaic original (or possibly Arabic), and mid-1st millennium BC at the oldest, (c) the language is influenced by older languages such as Ugaritic, making Job a very old book, and (d) the language was deliberately made foreign-sounding, because the book is set in the land of Uz, far to the east.
Modern scholarship assumes that the book borrows the name of Job from Ezekiel or other tales of Job, and different parts of the book were composed over a few hundred years across the mid-1st millennium, which makes the oldest parts of it quite old, but newer than the oldest books. The oldest complete book appears to be Hosea - parts of some of the other minor prophets and Isaiah appear to be similarly old, but those books contain newer sections in addition to the older parts. The oldest text in any book of the Bible is often assumed to be the Song of Deborah,