Is there any phrase or idiom for "impossible to find out about something"?

Solution 1:

The nearest English idiom I can think of is "God only knows".

(You might think the word order should be "only God knows", but the idiom has it the other way.)

This idiom gets used in both trivial and serious contexts. The literal meaning is of course that only God would know the answer, but it is also used figuratively to refer to things that might be difficult but not completely impossible to find out.

It can can be used in response to a question, e.g.:

"Where did they stash the loot?"
"God only knows."

Or as part of a statement (typically expressing frustration at not knowing):

"God only knows where they stashed the loot."

Some people shorten it to "God knows". Another equivalent expression is "Heaven knows."