A mathematical model of what this might look like: you might have a candidate class of formal models U that you think of as "all GAI" such that you know of no "reasonably computable"(which you might hope to define) member of the class (corresponding to an implementable GAI). Maybe you can find a subclass F in U that you think models Friendly AI. You can reason about these classes without knowing any examples of reasonably computable members of either. Perhaps you could even give an algorithm for taking an arbitrary example in U and transforming it via reasonable computation into an example of F. Then, once you actually construct an arbitrary GAI, you already know how to transform it into an FAI.

So the problem may be factorable such that you can solve a later part before solving the first part.

So, I'd agree it might be hard to understand F without understanding U as a class of objects. And lets leave aside how you would find and become certain of such definitions. If you could, though, you might hope that you can define them and work with them without ever constructing an example. Patterns not far off from this occur in mathematical practice, for example families of graphs with certain properties known to exist via probabilistic methods, but with no constructed examples.

Does that help, or did I misunderstand somewhere?

(edit: I don't claim an eventual solution would fit the above description, this is just I hope a sufficient example that such things are mathematically possible)