In order to prove a negative, you need to demonstrate that the biblical figure is mentioned nowhere outside the one ancient book that contains information about him, and then show that the book is not historically true.
In most cases, the absence of any information about a famous person from the past can be explained away by the paucity of extant records from the relevant period, or simply that the person was not of sufficient repute to have been mentioned by most of his contemporaries. However, plentiful records do exist from both Babylon and Persia. And if Daniel rose up to become the second most powerful person in the Babylonian Empire, then soon after became the second most powerful person in the Persian Empire, there ought to be many manuscripts and tablets that mention him. Yet there is no mention of him in any other Hebrew writings, nor in the extensive Babylonian and Persian records available to scholars.
Leonard J. Greenspoon, in 'Between Alexandria and Antioch: Jews and Judaism in the Hellenistic Period', published in The Oxford History of the Biblical World (edited by Michael D. Coogan), page 322, describes the Book of Daniel as a Jewish novel. This view, also held by most biblical scholars, is partly based on the book's historical errors and fragmented authorship. A very clear historical error is to be found the account of the Persian conquest of Babylon, in Daniel 5:31: "
And Darius the Median took the kingdom, being about threescore and two years old." It was Cyrus the Great who conquered Babylon. Darius I was a successor who followed Cyrus somewhat later, but Daniel 6:28 places Cyrus after Darius. An error in respect to Belshazzar is explained by the Jewish Encyclopedia:
The following important differences between Belsharusur and the Belshazzar of Daniel are patent. The former was the son of the last king of Babylon [Nabonidus], but never reigned, except possibly as coregent with his father; while the latter is distinctly called the last king and the son of Nebuchadnezzar, both of which statements are undoubtedly made in perfectly good faith by the author of Daniel.
The chief character in a work of fiction is often not a person who ever existed. Parallels to another Daniel briefly mentioned in the Book of Ezekiel point to Daniel as a literary creation.