Daniel Marsh:
How does one know that the Bible is inerrant?
Don’t confuse inerrant with infallible.
Things of this kind can’t be known - only believed.
There is no way of knowing that Christ is in the Eucharist, that the Bible is inspired, or that Jesus is indeed God.
There is no such thing as knowing beyond all possibility of doubt or mistake that anything whatever is true - every claim to knowledge requires faith, of some sort. I don’t know that sentence even makes sense - I have faith that it does

I don’t know that you are not a Martian - I just have no reason to think you are.

Do I know that I am a human being ? No. I could be a Martian; Martians may be indistinguishable from human beings. And so on; nothing whatever in this world can be known.
There are different degrees of probability, but no more. It is conceivable that that WW2 was a massive illusion - improbable in a very high degree; but not impossible. That is one of the reasons people can seriously maintain that the 1969 Moon landing was faked, or that the Shoah never happened: and those are both events in living memory.So it’s a pretty safe bet that, a few hundred years from now, scepticism about the Nazi murder of the Jews will become quite respectable, because there will be no one to “blow the gaff” - no survivors of Dachau or Belsen to say otherwise.
So with the Gospels - it has been perfectly possible to maintain in all seriousness that Jesus was a myth and the Gospels sheer invention; there are no Apostles to “blow the gaff”. It’s entirely possible - however unwelcome the suggestion may be to some - that the Apostolic Churches completely misunderstood the message of the Apostles, and turned a purely human crucified and dead Jewish Rabbi into a pre-existent dying and rising Divine Saviour: an inerrant NT is not much use, if it is an inerrant record of a misunderstood message; there is a lot more to arguing for inerrancy than inerrancy, but this is routinely overlooked.
That Jim Carrey fim about a man living a completely artificial life without knowing it explores the same difficulty of not being able to know that appearances are trustworthy.
This inescapable lack of knowing beyond all doubt is the reason we need faith to do or think anything - and Christian faith is only a special application of this need for faith.
One can have certainty even so - certainty does not require knowledge. Which is just as well

So lack of knowing, does not hinder action; the Gospel can still be preached, even though it cannot be proved. IMO, Christians worry about proof and knowledge far too much; to do so risks putting the emphasis on our poverty, and not on the richness of our God. The sooner we get out of the lime-light, the better
Faith is in a Person - not in statements. Christ can be known, because He comes into us and our intellects in a way which is more immediate than the way statements do. We have to reason our way to conclusions, and then convert the conclusions into statements so that they become communicable to others. But Christ is immediate, quicker than thought: He is the Way by which we go to Him, as well as the End of our journey; and His knowing of us, precedes our knowing about Him, and is its Cause. That, ISTM, is how we know anything - because He knows us: His Light relieves our darkness and ignorance. ##