No, that is NOT what science is supposed to do.
Scientific theories can NEVER be "proven" in the sense that theorems in Mathematics are proven. That would require making EVERY possible observation and conducting EVERY possible experiment that could dis-prove the theory.
Scientific theories are "accepted" based upon their consonance with the existing body of data, AND their ability to accurately make useful, falsifiable predictions. A theory that is subjected to multiple broad attempts to falsify it, and which explains the phenomenon within it scope better than other theories is thus "accepted" by the consenus among the scientific community.
In short, proof has nothing to do with it. It is based on the preponderance of the evidence, and lack of dis-proof.