We'll strip some power from the almighty 'theory' and make it a relative thing rather than an absolute thing. Like a court of law where the burden of proof is quantified by the term 'reasonable'. Also, strictly speaking, you cannot ‘PROVE’ a theory.
Okay, we should probably clarify what exactly we mean when we use the word ‘theory’ so first let’s go over some basic definitions relating to the scientific method so that we are on the same page with respect to meaning. The scientific method is simple: hypothesis, experiment, conclusion, repeat...
There’s probably a much better definition somewhere, but a ‘hypothesis’ is basically a (scientific) statement that describes or explains a specific, but complex, phenomenon and can be considered in opposition to one or more alternative statements.
You could argue that a theory is a just a ‘super- hypothesis’ –or you could say that it’s a major hypothesis of ‘great scope and importance’-- that has successfully met all (or most) of the challenges that have ever been put to it.
(NB. -just recognize that when I say "of great scope and importance" that that phrase is fully loaded with lots of anthropocentric bias!)
In one sense, you could consider a theory to be a major hypothesis that has achieved a special distinction and a fancy title... a theory is sort of like a hypothesis that has been ‘knighted’ let’s say... so now Paul McCartney is "Sir Paul McCartney". And the ‘hypothesis of evolution by natural selection’ is elevated to the status of the ‘Theory of Evolution’. Although it might be less conventional it wouldn’t be incorrect to still use the term 'Big Bang hypothesis' rather than the term ‘Big Bang Theory’. Furthermore, there’s a chance, very small in some cases, that a theory that has been around for a while turns out to be "wrong" in specific circumstances. That reiterates the theme that science is a dynamic enterprise and so it should be/ must be!
Here’s a specific real example: two metal plates, being electrically neutral would have no charge between them, right? But Henry Casimir found that the vacuum between them, due to Heisenberg’s Uncertainty Principle, was teeming with disappearing/ reappearing particles and antiparticles... and using quantum theory he showed that there could be negative energy between the plates... totally contrary to classical electricity but the empirical tests showed that the Casimir Effect occurred exactly as QM had predicted. So the standard formalism ("old truth") gets replaced by the "new truth".
Relativistic physics showed that to be the same case for the Newtonian model of gravity... but because relativistic formulae are so complex, a NASA engineer would still use the old formalisms (Newtonian kinematics) for calculations involving simple satellites etc. Which really underscores the utilitarian view (call it pragmatism or logical positivism or realism) that the "correctness" of the theory is only important up to the point that the theory is useful and predictive— it doesn't matter to the strict utilitarian whether or not the theory is an accurate representation of some independent objective reality. So science as an epistemological endevour is a changing and dynamic thing that perhaps uses a notion of "relative truth" rather than the (unattainable) absolute truth.
And of course that leads inexorably to some deeper (ontological) questions— namely given the epistemological methods of science, what particular ontological model do you as an individual accept? And why?
... but that’s a whole other topic!