Leonard J Greenspoon says in ‘Between Alexandria and Antioch: Jews and Judaism in the Hellenistic Period’, published in The Oxford History of the Biblical World page 322, that, at least in its finished form, the Book of Daniel was a Jewish novel. Its authors or compilers were not intent on relating actual events of the past, nor did they expect their audience to understand the book as historical. Although we may find an answer within the text, we should not regard that as historically correct, nor should we expect corroboration from any independent source.
In Daniel chapter 3, Nebuchadnezzar demanded that everyone in the kingdom worship a great idol that was set up on the plain, whenever they heard the music. But he was told that Daniel’s friends, Shadrach, Meshach and Abed-nego, refused to worship the idol or pay homage to the gods. They were brought before him and told that unless they worship as required, they would be thrown in a fiery furnace. The boys were bound and taken to the furnace, but it was so exceedingly hot that it killed the men who held them. The king saw the three, alive and in the company of an angel, in the midst of the fire, without even a hair singed or their clothes burnt. He then ordered that anyone who spoke against the God of Shadrach, Meshach and Abed-nego be cut to pieces.
Notice that the text brings to our attention that the fire "was so exceedingly hot that it killed the men who held them," making it all the more miraculous that the young men survived unscathed. Then we are told that Nebuchadnezzar honoured the God of Daniel and his friends, a point made even more forcefully in chapter 4 and again, with a different king, in chapter 6. Greenspoon says (ibid, page 341) that the Hebrew form of Daniel neatly divides into two parts, with chapters 1 to 6 consisting of a collection of tales, in which Daniel and his companions demonstrate the superiority of their God and those who obediently follow him over the worshippers of false, empty and powerless deities.
The Book of Daniel does not tell us where Daniel was at the time the three young men were cast into the furnace, so that information is unavailable to us. However, it could be noted that if Daniel had been included in this scene, and so cast in the fire, then the very similar drama of his being cast into the lion's den would be lessened. For literary reasons, he needed to be elsewhere.