Impossibility is when something can't fit into a logical framework.
A triangles angles can't add up to 185 degrees under euclidean geometry.
Since euclidean geometry is a closed mathematical system, one can prove whether something is actually possible from it just by seeing if a statement follows from its the systems axioms.
All evidence points to the universe also having an axiomatic system that it is based on. Since humans probably will never get the universe completely figured out, deciding whether or not something is possible can be guessed to an unknowable (but high) accuracy. Possibility shouldn't be confused with scientific probability. If anything is scientifically probable, it is also possible.
For example, one could say "is it possible for time to suddenly reverse on all of us randomly?" The scientific answer would be no, because it violates many scientific laws, especially causality. Is it actually possible? Probably not. To see evidence that it is possible one would either have to see physical evidence of a similar event happening or see evidence that some of the theories that it violates are wrong. Since there is no evidence of time suddenly reversing (either through direct evidence or induction through axioms) and we also have an incomplete picture of the universe, it is not possible to conclude on its actual possibility.