Consider the claim:
Science is the only way to discover truth.
Is this science? No. What experiment shows this? None. It is a self-defeating statement. Consider a modified claim:
No method other than science has been shown to discover truth.
This statement is no longer self-defeating. But what is meant by 'truth'? Let's say "how reality works". We consider F = ma to be 'true', at least in certain domains. In others it's an alright approximation, and others it's a terrible one. It seems best to think of this kind of 'truth' as "true under these circumstances". Surely though, my inner thought-life is part of reality. Can science understand how it works? Somewhat. Can I say true things about it apart from doing science? Herein lies the rub.
If we define 'truth' as "what science does", then we essentially say that a color is only 'red' if it has sufficient 'redness'. A claim is only true if it is sufficiently investigable such that science can be done on it. But these leaves huge swaths of life where science can't be done (many events in people's lives are nonrepeatable and not sufficiently similar to other events), or oughtn't be done (let's see what happens when infidelity is encouraged, under controlled settings). Do we really want to deprive ourselves of the concept 'truth' in these areas?
I suggest a significant reframing:
Scientific claims are less likely to be wrong than unscientific claims.
This, I suggest is virtually a tautology. Something is considered 'scientific' when it has been shown to model reality sufficiently well. That is, when the amount of time the model is wrong passes below a certain level, it is considered 'science'.
This also says nothing about whether scientific claims are Absolutely True. That is because they are not: too much 'accepted wisdom' has been disproved, time and again, for very many good scientists to make claims to absolute truth. Stephen Hawking and Leonard Mlodinow coined the term model-dependent realism, in a sense capitulating to possibility that there isn't One True Way to describe How Things Are.
For fun, I suggest asking whether the philosophy of Atomism was helpful to scientific endeavor. If it were, I suggest that calling something 'true' only after science has verified it (or attempted to falsify it) is tantamount to saying that something is only 'food' after it is served—not when it is in ingredient form. We can define our terms this way, but doing so might hide the fact that we need things in addition to science to discover what is true. Just like the newscaster needs a huge support staff to do what he does. Valuing only the last stage of a process is a great way to do the process poorly.