We know plenty of actually very simple problems that we would not be able to solve from now till the Sun explodes even if we all of the computers on earth were only doing this. Say, solving a worse case instance of the Knapsack problem for n > 250 items easily fits into this.
If you want to be precise, the complexity class EXP best fits my description (though NP-complete would also be enough). That is, if discovering the required technology to build a self-replicating interstellar probe requires solving an instance of an EXP problem that is not ridiculously tiny, then we would likely never be find out how to build this probe. And no amount of AGI would change this, in this case.
I'm not suggesting that I have any reason for this ridiculously precise scenario to be correct. Just that some technology being allowed by the laws of physics should not be taken to mean that it is actually implementable in any imaginable amount of time, even if we were to assume singularity-style AGI.