In the first half of the 20th century a group of philosophers, called Vienna Circle, discussed the question: How to establish a border between science and metaphysics.
Prompted by their discussion but in contrast to their findings the Austrian philosopher Karl Popper stated the following demarcation criterion:
The difference between scientific and metaphysical statements is the fact, that the former can be falsified but the latter can not.
For Popper’s thesis see his book „The Logic of Scientific Discovery“.
Popper‘s thesis is in accordance with the fact, that scientific theories like the Theory of Relativity and Quantum Theory are open to falsification by observation. Up to now, these theories have not been falsified, there are no observations which contradict these theories. But we can identify there domain of validity.
On the other hand there is no scientific theory which includes Big Bang as an event. Big Bang is a limit of the cosmological standard model. But Big Bang is not part of the theory, because several physical quantities become tend to infinity when approaching Big Bang backwards in time. However, there are some scientific speculations how to embed Big Bang into a cyclic cosmological model.
The status of String Theory is highly debated. It is unclear whether String Theory makes any observable predictions at all. The question is whether String Theory is metaphysics or science. But in any case, String theory relies on an interesting mathematical theory.