As I understand it, it is not possible for a human to design a machine that is "smarter-than-human", by definition.

Then we couldn't design a machine that could design a machine that would be smarter than we were, either. Machine-2's design couldn't be smarter than it, and machine-2 couldn't be smarter than machine-1 which designed it, which in turn couldn't be smarter than the designers of machine-1: us.

We can't hold in our individual minds a design that is more complex than one of those minds, or in our collective minds what is more complex than the collective. But the design doesn't have to be as complex as the thing that is designed, and the representation of the design is simpler still.

It's trivially easy for a human being to design a data-encoding-and-storage system that can hold more data than is contained in that human's brain. The brain just can't represent that system.