Certainly the mind can conceive a theorem or proposition as true or false before a proof has been undertaken, just as it conceives that objects continue to exist when out of sight. Theorems may be intuited as true, even though unprovable in any known system, just as some physical entities may be suspected to exist, though never observed. In contrast, provability is always relative to some particular formal system. By definition, it is decidable for all complete systems. Since proof means derivability from axioms, no system can prove its own axioms, but can only justify itself as convention or by appeal to some outside reality.
Truth refers to such a reality beyond the pale of a given system.
To lie beyond a specific system is quite different than to lie beyond all possible systems. We can always find and specify a formal system larger than any given one. But our intuitive idea of truth is that it lies beyond all formality, beyond all limitation, beyond all human creation. Existing in and of itself, truth is transcendent reality. Such truth can be approached but never reached, because it can never be fully specified.