God did not send us a “book” down from heaven.
If the Bible was absolutely “perfect” than we would all have irrefutable scientific evidence for the existence of the Christian God. The “book” as our “proof” would reach the esteem of being an object to worship, kept only in the original language, and be the source for everyone to become Christian. People would put their trust (faith?) in a book (you might look at how the Muslim’s treat the Quran.)
In God’s wisdom; God would not allow the “Bible” to become what it was not intended to be.
You bring up some good points and ask good questions.
“Proof” or at least strong “evidence” for a god is what the agnostic, atheist, and/or skeptics is asking for and think they need to at least “believe”. They do not really want to “believe” (trust/ have faith in), but have “knowledge” of God existence. The problem is “faith in a benevolent Creator” is needed to help the individual with his earthly objective and really cannot be completed without it.
What you have to always keep in mind is the objectives:
Man’s objective seems to be to obtain and grow this Godly type Love to fulfill the mission (statement) of Love God and secondly others with all our heart, soul, mind, and energy.
This Godly type Love is defined by Jesus’ words and deeds (you can also use 1 Cor 13 and 1 John 4).
Since God is “Love” and part of the definition of Godly type Love is unselfishness God is totally unselfish? If God is totally unselfish, He will do and allow all He can to help those that are just willing to accept His help fulfill their objective (Love). That “all” includes: Christ to go to the cross, satan to roam the earth, tragedies of all kind, hell, evil, and even sin.
God is not trying to trying to get us to do something, but is trying to give us the most powerful force in all universes if we will just accept the gift as it was given (charity). Having Godly Love is having the most powerful force in all universes.
Will we know people do not like to accept charity especially from a giver that paid a huge price? People will try to earn the gift, pay back the gift, be more deserving of the gift than the next person or just say they got the gift without having to accept it. The easiest way to accept the gift is through accepting God’s forgiveness (this is after you have sinned) since forgiveness is charity, grace, mercy Love. AND Jesus has taught us “…he that is forgiven much will Love much…”
Faith in just the existence of a Creator takes very little trust and is something we really would want to do at least to relief this burden we carry from hurting others (sin) in our past. That turning to trust in a benevolent Creator is a humbling action (something the lowliest person on earth can do) and that humility is enough to allow us to accept God’s Charity. The easiest way (God set this up) is to accept God’s Charity in the form of accepting God’s forgiveness (Love/Charity/Grace/Mercy).