The set of "Knowable reality" encompasses far more than the set of "truths".
Perhaps we have a definitional problem to overcome. If something is, if it exists in reality, then a statement that it exists is a "truth." If something is of value, "x is better than y," then this statement of its value is a "truth."
I'm defining "truth" as what is true in reality. I would reverse your statement and say that we cannot, likely, know all of reality (humans have finite limits). So "knowable reality" would be a subset of all truth about reality.
"Most of the universal "truths" do not exist yet in the set of "knowable reality".
"Most" and "universal" would need clarification. I'd start with substituting "absolute" for universal. "Most" we could leave out of consideration for now, I think. (We'd have to deteremine the set of all absolutes, and that might distract from the basic discusssion.)
We can however know some very basic absolute truths. In fact, it is impossible for self-conscious humans to act without at least assuming some absolutes. The alternative, all conditional truths, must have some absolute on which to begin. All of us act as if we have knowledge of basic absolute truths, yourself included.
"Science is the job of moving those "truths" into that set."
Only a subset of all possible knowable truths: those that can be known using through the physical senses (and their extensions-telescopes, microscopes…)
This strict sense empiricism must leave out "values" (in the sense of better than). For example, one molecule is not better than another, life is not better than death (except for its utility to the experiment). This is how science should and must be. It's its strength, but also its limitation.
So science is the firmest form of "truth," yes, but it is not the only truths we can know, and as I've said, we cannot function with what can be known by the senses alone.
There are things that can be supposed/theorized or be articles of faith. These may be treated as reality but it does not transform them to provable "truths".
Provable using scientific method? No, of course not. Only those things that can be known through sense empiricism (as well as having number, size and simple location) can be known by science.
Again, science is the most firm knowledge, it is the knowledge of rocks, material. But we do not wish to limit ourselves to this subset of knowledge. If we did, for example, we'd have to leave out a great deal of what you think of as science. Science itself has to take a great deal for granted, supposed/articles of faith. For starters, that the universe is everywhere consistent and that we can trust our sense experience. These cannot be proven using science alone.
"We learn to deal and find practical use everyday for things we do not understand."
And one of the ways we deal with reality everyday is to know, or assume we know, absolute (unconditional/non-scientifically-provable) truths. We can act as though we know them unaware that we do so; we can choose to assume them based on other people's view; or we can explore what we can know about them for ourself, by direct personal experience, and by then comparing results with others examining the same areas.
The latter route is one definition of religion: the exploration of absolute truths through empiricism. It's the definition of religion that I prefer, though it is not the one in popular use. Still it's a very common method, or practice, of many religious folks around the world for many centuries.
It's likely the method of religion that would appeal to many of a scientific bent - like me - perhaps you too. Though many scientists are not at all interested.
Still, scientists should not make the logical error of going from "it cannot be known by science" to "therefore it does not exists."
I prefer scientific "truth" to mean that which exists independent of the perceptions or thoughts of humans.
I prefer "reality" to encompass the entirety of the world as perceived by, thought of and acting upon humankind.
For instance, the unknowable, or unprovable, may be treated as an article of faith by an individual. As such, that faith does indeed form a part of his reality. Yet it may be directly counter to the faith of another individual.
That these two "faiths" exist is real, but that does not render both of them "true". (Hence, the motivation behind so many religions to "prove" their own faith to be true by disproving the faith of the other.)
For me I readily accept God as real and true. I pursue science as a means to learn more about the truth of Gods universe. I do not fear "truth" conflicting with my faith, because those truths could only be correcting human misunderstanding. (Humans err, the truth just is.)
I can accept an article of faith being shown to be false. Only a greater, stronger faith can thus evolve.