Everyone trusts in Eru?

I've seen a lot of people in the thread "Was Gollum's slip the only way?" discussing the sheer absurdity of the task lying before Frodo. Literally, none but the most pure could perform a feat as great as throwing the One Ring into the Crack of Doom.

Gandalf, in the center of his being as Olorin, knew always that there was no hope for Frodo to throw the Ring into the Fire - it is an impossible task. (Given that Frodo and Sam overcame the ridiculously dangerous journey to Oroduin.) Yet he always maintained that there was hope for the Quest.

In this I can see nothing but absolute faith in Eru. Just as on the Bridge of Khazad-dum, Gandalf surrendered to his God and placed the entirety of his Mission in the hands of Eru. A heavily contested argument is that it was by the designs of Eru - in whatever way - that caused the Quest to destroy the Ring succeed.

(HALiverpool did suggest in the thread "Was Gollum's slip the only way?" that the power that caused the Ring's destruction was the Ring's own bond and curse. An excellent idea, although I personally am still convinced of the belief that even if this is true Eru was still fundamentally involved in such a circumstance.)

My question, given the involvement of Eru, is this: For what reason did every other member of the Wise than Gandalf (who is one of the very servants of the Secret Fire) trust in Eru's help? Surely it is blind trust. This is something I have never witnessed before in Middle-earth. They knew that of aid from the Valar they could reasonably expect nothing more than the Istari without causing more turmoil to Arda. Even the aid of the Valar was often spurned in the Elder Days. So to think that the Valar could aid Frodo in his insane quest would be irrational.

But who else could Galadriel, Elrond, and the other Wise rely on? Had they ever relied on divine forces/sheer chance working for them? When there can literally be no other way for them to succeed?

Never can I recall such a Kierkegaardian feat of faith on the behalf of so many characters of JRRT's writings.