How did Daniel receive the interpretation of Nebuchadnezzar's dream, and what does that show about God's role?

The secret was revealed to Daniel in a night vision, after he requested time from the king. This demonstrates that the almighty sovereign God was at work, not human happenstance, giving Daniel the forgotten dream and its interpretation. Daniel testified that there is a God whom Nebuchadnezzar knew nothing of.

Les explains that Daniel was still a young man, without gray hairs or age-based respect, yet he answered Ariok with counsel and wisdom and asked the king for time so he could show the interpretation. Then the secret was revealed to Daniel in a night vision. Les emphasizes that this was the almighty sovereign God at work, not human happenstance. God revealed to Daniel the dream Nebuchadnezzar had forgotten. When brought before the king, Daniel confessed that the wise men, astrologers, magicians, and soothsayers could not show the secret, but he testified that there is a God—the God Nebuchadnezzar knew nothing of.

Daniel 2:19

Then was the secret revealed unto Daniel in a night vision. Then Daniel blessed the God of heaven.

Was the revelation of Nebuchadnezzar's dream to Daniel a coincidence?

The revelation was not a coincidence. It was the almighty sovereign God at work, revealing to Daniel the dream Nebuchadnezzar had forgotten. The secret was revealed to Daniel in a night vision. Scripture presents it as divine intervention, not human happenstance, demonstrating God's sovereign control.