Maybe that negation would be too obviously related to the idiom. There are other ways to say there is a way; e.g. instead of shikata, there is houhou： 方法　（方法がある）.

The counter-idiom, if you will, to "nothing can be done" might be "where there is a will, there is a way":

意志のあるところには方法がある。

If someone says しょうがない　or しかたがない, and you don't agree, that might be the thing.

> The counter-idiom, if you will, to "nothing can be done" might be "where there is a will, there is a way":

I've always thought of the counter-idiom as being やればできる (yareba dekiru) -- "you can do it if you try."

Sounds like it's a thought-terminating cliche- of which we have many in English.

well, that's just the way it goes.

"It's God's will."