In Star Trek TNG S02E02 the Enterprise and its crew are trapped in a void by a mysterious and extremely powerful entity known as Nagilum, who wants to learn about them.
At the end Nagilum tells Picard that humanity is arrogant, militant, etc. Picard responds to him that at least they have one thing in common, curiosity.
Could Nagilum actually have been Q?
Highly unlikely
For one, every time we see the Q, the Q aren't too shy to announce who/what they are, and Nagilum never does so. Also, all the Q always emulate human(-oid)s, and Nagilum doesn't do that either.
Also note that the Q are far from the only sheer-omnipotent beings in space. For instance the Douwd (as seen in TNG S3E03) are pretty powerful too. Nagilum can simply be a member of an unknown, to our minds quite powerful species. Or just a completely singular being.
Nagilum was a creature made of pure energy living "outside of the universe", and the encounter with the Enteprise-D was the first contact between humanity and him. This is the reason why he "studies" and "experiments" with humans aboard the starship.
Humanity, and the Enterprise-D crew in particular, already had the chance to meet the Q's previously.
Apart of their apparent godlike powers and omnipotence, there is nothing in common between these two creatures/species, and Nagilum is never referenced later outside this episode in a context that could link him to the Q's (or to any other species, for that matter).
It's not stated if Nagilum was truly omnipotent. If so he could have stopped the self destruct..........Or simply didn't want to test their resolve and capacity. But he's not the Q. Upon judging humanity and assessing his findings. He is also "Ignorant" of processes outside his universe, such as death. The Q are omniscient of circumstances.
