Personally I prefer no explanation over a really stupid explanation.
Presumably Q operates in some manner which is scientifically logical, we just never get that explanation and it would probably be something that humans literally would not be cognitively equipped to understand. Q is to humans like humans are to dogs. Whilst I can communicate with my dogs there is a wast universe of things my dogs could never understand, or even imagine. Even the smartest of my dogs couldn't ever understand how a combustion engine works or that Moon revolves around Earth. I find it fascinating that there could be beings that would cognitively be in similar manner beyond humans.
Given that Q was a product of Season 1 TNG, there is zero chance that there was an elaborate backstory behind his character. However, I'm sure the writers would be elated to hear your kind words about him.
After the fact, we fill in the blanks with our wildest imaginations, creating backstories and concepts that were never there to begin with. This has happened with other random things, too, giving fuel for a great many novels covering all kinds of ST topics. After the fact.
It's always fascinated me how people (including myself) fill in the blanks when there's a stark lack of information. Suddenly a shallow character can become one of the most complex ones, simply by virtue of the viewer's imagination, not the content of what's actually seen & heard. Part of me wants to applaud such things that fuel the imagination, and part of me wants to slam lazy writing. Hard to pick.
In politics, people say it's sometimes better to not have a voting record. That way, it's easier for voters to imagine you as the very best of their ideals. They "fill in the blanks" based on those hopes. When there's a voting record, it gives people something to throw stones at. Instead, with a lack of information, you could be the maverick, the challenger to the system, the unifier, etc., and the otherness of it is exciting to some folks.
As I said early on in the thread, I love mystery - like the mystery of who the Red Angel could be - but eventually we expect there to be answers. Some people embrace the mystery of Q while also demanding immediate answers to the spore drive questions. Use your imagination and also strap in for answers that won't be nearly as cryptic as Q.