It is very possible that the information necessary already exists, imperfect and incomplete though it may be, and enough processing of it would yield the correct answer. We can't know otherwise, because we don't spend thousands of years analyzing our current level of information before beginning experimentation, but in the shift between AI-time and human-time it can agonize on that problem for a good deal more cleverness and ingenuity than we've been able to apply to it so far.

That isn't to say, that this is likely; but it doesn't seem far-fetched to me. If you gave an AI the nuclear physics information we had in 1950, would it be able to spit out schematics for an H-bomb, without further experimentation? Maybe. Who knows?