How to know for sure if we can learn from a given data or not?
how can we know for sure


We can't. 
A toy example to show why even humans can not do this for sure:

Assume you get the number 2, 4, 8, 16, 32, ?? and want to extrapolate to the next number ??. A natural extension of the series would be 64, but we can not take this for granted. The next number can just as well be 0. You can not be sure. 

Only given the data and without additional assumptions about what you would expect to see, you can not learn a correct model per-se. You always have to be critical about your data.