In the context of structures from ancient civilizations, design is inferred based on relative comparison of natural forming objects with specific human construction. In the case of something like ancient Egypt, we have ample evidence of human civilization and construction techniques. Even if the specific techniques are not known for a particular structure, we have enough evidence to infer such.
and even before we did, as a complete mystery- people still recognized they were built- even if 'by aliens' as some might claim

because although they are extremely simple, the design represents information which specifies something beyond a heap of sandstone- or anything nature might create in this context
to be precise, it specifies 'this is a pyramid'
This is a silly example, since any and all envisioning of alien spacecraft is entirely based on human imagination. IOW, we're inventing what we think those things look like.
The truth is, we have no idea what a real alien spacecraft would really look like. And for things like SETI where we are trying to detect alien signals, we infer such based on our own technology.
"we infer such based on our own technology." well yes, as we might 'infer' intelligence for hierarchical digital information systems we see in biology! but I'm saying that
similarity is not good enough for my argument- that it is far too easy to see faces in clouds.. That we can refine the evidence to something far more definitive and objective than mere familiarity. Where the key fingerprint is information itself- no matter how exotic, mysterious familiar or unfamiliar, the medium, source, construction technique -- all these may or may not seem to 'infer' artificial or natural mechanisms from our common experience. But we can put this subjectivity aside and look at the pure mathematical value of the information, the signal to noise ratio, what is more objective than math itself?
The typical methods for inferring design is looking for signs of deliberate manufacture (relative to naturally forces). And that itself relies on foreknowledge of what that manufacture could look like and basic pattern recognition.
Nobody is looking at a pyramid and thinking, "hmm, I wonder what the information content of that structure is".
I agree entirely, we don't consciously evaluate the information quality and quantities in Mount Rushmore v the Old Man of Hoy before concluding that one is artificial and the other is natural
we intuitively know this from familiarity of precedent in such obvious cases.
But what if the context is unprecedented? the only instance of a particular phenomena we have ever encountered? like life, the universe and everything as Adams would put it?
We need an objective measure that utterly discounts what merely seems familiar or 'looks' natural or artificial to us- how else to approach this?