This is akin to a Greek of 5th bce asking Leucippus and Democritus how we could know the structure of a world we cannot see.
The absence of an answer is not proof of nonexistence or impossibility. It is just neutral absence. Absence as evidence is only """ valid""" when all possibilities are exhausted in a definite way. Outside of math, that threshold is exceedingly rare in problems of even moderate difficulty.
Moreover, this style of inquiry can easily be turned on its head and used to (apparently) redress the interlocutor... Neither are worthwhile endeavors.
Just curious, can you think of a non-contrived, moderately difficult, non-mathematical problem that has or even in principle could be settled through abscence of evidence? Especially a positive assertion. Closest I could come up with is say confirming a diagnosis by elimination, through abscence of evidence of other candidate diagnoses. But even then there's a non-zero possibility that it's a hitherto unknown disease, or that there was some false negative somewhere.
The absence of an answer is not proof of nonexistence or impossibility. It is just neutral absence. Absence as evidence is only """ valid""" when all possibilities are exhausted in a definite way. Outside of math, that threshold is exceedingly rare in problems of even moderate difficulty.
Moreover, this style of inquiry can easily be turned on its head and used to (apparently) redress the interlocutor... Neither are worthwhile endeavors.