Unless you believe humans have something mystical like a soul, our brains are evidence that “general intelligence” is achievable in a relatively small, energy efficient form.
Actual AGI presumably implies a not-brain involved.
And this isn't even broaching the subject of "superintelligence", which I would describe as "superunbelievable".
Come up with any goal you want to reach, and some human can but a large dent in the problem. Maybe reach the goal outright.
We already have some nifty artificial goal to action mappers. None of them are generalized to a wide category of goals yet. Maybe some goals need consciousness to be reached, but that isn't a given. We don't really know that. We might be left very unsatisfied in the way an artificial goal to action mapper reaches any goal without consciousness. We might even call it cheating.