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ctintera comments on Stupid Questions December 2014 - Less Wrong Discussion
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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.
Evolution is an optimization process. It might not be "intelligent" depending on your definition, but it's good enough for this. Of course, that just means that a rather powerful optimization process occurred just by chance. The real problem is, as you said, it's extremely slow. We could probably search it faster, but that doesn't mean that we can search it fast.