My question arises from the growing concern that many people seem to overlook the vast amount still left to discover in science,
True
leading to an overestimation of its achievements.
Who overestimates? Not the scientists for sure.
Increasingly, there is a tendency to assume that anything not scientifically proven is inherently false.
This is not increasing - this is the basis of science. Either you follow it and you are a rational person, or you don't and you are not rational. Both are OK, we agree to disagree.
However, this raises an important question: if a phenomenon cannot be tested, does that make it false?
To a scientist, this "phenomenon" does not exist. Yo may belive that on the other side of the Moon there is a chakra factory but until it is measured it simply does not exist to a scientist.
We are not saying that this is false, just that since we do not see it, well, we do not worry about that too much (very roughly speaking)
Why is it that so many people believe science to be the ultimate arbiter of truth,
Because this is how science works, if you belive in it
when in reality, science is still in its relative infancy?
Relative to what?
What I find particularly troubling is the authority that science has seemingly acquired—the belief that it can eventually explain everything.
We certainly hope that we can explain everything we discover. There are plenty of things we discovered that we cannot explain, though, because w do not have the knowledge to do that yet (and we may never have;, if we are too dumb of if there is a fundamental flaw in the way we perceive science).
The thing is that these unknown / unexplained areas are at the border of our knowledge. When someone says "ghosts" or "telekinetics" then we shura can measure it and this was done many many times.
Yet, it seems possible that certain truths may exist that science is inherently unable to validate.
Such as? It is either something tangible we will measure and push into our theories (possibly modifying them) or it is not (god created the universe) and we do not care.
Why, then, is there a prevalent perception that truth must always align with scientific verification?
Not sure what you mean by truth. There is no truth on not-truth in science, there is a theory, a model, measurements of things happening and either the measurements fit or they do not fit.
At least physicists dream of things that do not fit. I publicly stated that I will switch my PhD thesis overnight if someone can show me a tangible event that is outside our view of physics (ghosts, tele-stuff, ...). Because you now, Nobel Prize. I unfortunately ended up with my boring thesis about particle physics.