Perhaps this is a special case of theodicy, or the argument from suffering, that certain kinds of suffering are logically incompatible with an omnipotent benevolent personal Creator.
Namely, “The Church’s message is too good to be true.” Even if I cannot disprove unverifiable miracle claims or ascertain ancient history, the goodness of the claim pushes it beyond what can be reasonably hoped for. In other words, this world has so much suffering that the claim that all wrongs will be righted appears to belong in another universe. (Perhaps this is in fact what St. Paul was writing about regarding the universe itself groaning for a new creation …? Romans 8:18-27)
So how would you answer this objection? “The Gospel (that God is love and will right all wrongs and reward the faithful beyond expectation) is too good to be maintained.”