And I doubt whether that is ever truly possible.
It's possible. We're an example of that. The question is if it's humanly possible.
There's a common idea of an AI being able to make another twice as smart as itself, which could make another twice as smart as itself, etc. causing an exponential increase in intelligence. But it seems just as likely that an AI could only make one half as smart as itself, in which case we'll never even be able to get the first human-level AI.
The example you give to prove plausibility is also a counterexample to the argument you make immediately afterwards. We know that less-intelligent or even non-intelligent things can produce greater intelligence because humans evolved, and evolution is not intelligent.
It's more a matter of whether we have enough time to drudge something reasonable out of the problem space. If we were smarter we could search it faster.
This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.
Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.
To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.