The clay cylinder that names the king Isaiah predicted
Isaiah named Cyrus as Israel's liberator roughly a century and a half before Cyrus was born. Then archaeologists found Cyrus's own account of a policy that matches it.
Among the boldest claims in the Old Testament is not a prediction of an event but a prediction of a name. In Isaiah 44 and 45, the text names a specific foreign king, generations before his birth, and states plainly what he will do: end Judah's exile, and issue the order to rebuild the temple in Jerusalem. The king is Cyrus. At the time the words were set down, Persia had not yet conquered anything, and would not exist as an empire for roughly a century and a half.
Skeptics have a ready answer for this, and it deserves to be stated rather than dodged: most critical scholarship dates the second half of Isaiah to the exile itself, precisely because it names Cyrus so specifically. That is a serious position, addressed elsewhere on this site. It is not the subject here.