Nebuchadnezzar was a pagan king whose ideas about the truth of the heavenly hosts was vague and influenced by his own polytheism. However, we have some clarification of what he thought a few verses later in Dan 3
- V25: “Look!” he exclaimed. “I see four men, unbound and unharmed, walking around in the fire—and the fourth looks like a son of the gods!” [Had this been uttered by a Hebrew, it would have been translated, "Son of God", but a heathen king said it.]
- V28: Nebuchadnezzar declared, “Blessed be the God of Shadrach, Meshach, and Abednego, who has sent His Angel and delivered His servants who trusted in Him. They violated the king’s command and risked their lives rather than serve or worship any god except their own God.
Now, notice that:
- Nebuchadnezzar believed this "son of the gods" was an angel
- The word "gods" in v25 is the same word translated "God" in v28 and is plural in both cases.
Thus, as many versions say via footnotes, and some in their main text (eg, KJV, NKJV, Brenton LXX, etc), V25 can reasonably be translated "Son of God".
As Christians we understand the significance of this phrase "Son of God", but it is just as certain that Nebuchadnezzar did NOT understand that the still future NT would apply this term to the Messiah.
But still the question has to be answered, What did the king see? The
early Patristic interpretation was that. it was none other than Christ
Himself. We have no means of ascertaining anything further, and must
be content with knowing that the same “Angel of God’s presence” who
was with Israel in the wilderness watched over the people in Babylon.
Barnes says something similar:
Was it an angel, or was it the second person of the Trinity, "the" Son
of God? That this was the Son of God - the second person of the
Trinity, who afterward became incarnate, has been quite a common
opinion of expositors. So it was held by Tertullian, by Augustine, and
by Hilary, among the fathers; and so it has been held by Gill,
Clarius, and others, among the moderns.