Science has limits and cannot answer all questions. give an example of a question that cannot be answered by science

Most limits in science lie with insufficient technology precision. example: studying strings in string theory is only through math proofs, and not on empirical data.

Some things will never directly be proved.

What happened before the Big Bang?

Are there multiple universes?

Some things cannot be observed.

The parameters of an atom can only be instantaneously observed and not tracked over time since particle physics states a particle can express different states at once. By observing the particle, you are affecting its state, so it can't truly be observed.