I have been thinking about your question and about what is really at the heart of it. I do not believe the term "blind' faith is really the proper way to express what I believe you are asking, but I think I understand what you are looking for. Allow me, if you will, to first offer this observation about faith and then I will give you an example from Abraham rather than Noah to illustrate my point. If you would still like to see how this show up in the example of Noah, I will be happy to provide that for you.
Faith is from the word πίστις which means 'to be persuaded.' The word is translated in the NT as both faith and belief and reflects two interlocking dynamics. The first is the mental acceptance of a set of facts. The second is the action that responds to that acceptance. Belief is the fundamental structure for salvation but belief is never presented in scripture as exclusively an intellectual exorcise. Biblical faith is more than just a simple acknowledgement of a set of revealed truths. Faith is always presented as a behavior structure that actively responds to the word of God. James makes the point that faith apart from obedience to the will of God is not faith. Faith is legitimized only when it is linked to action. We see this in a number of examples given by the Hebrew writer. In Hebrews 11, belief/faith is inseparably linked to an active response that legitimizes what the mind has accepted as true. Without obedience to the will of God, there is no acknowledgement of faith. By faith those offered as examples of faith did what God commanded. Abraham And his sacrifice of Isaac is one of the examples given by the Hebrew writer.
There are truths we can understand from our observation of the natural world, but there are also truths that cannot be ascertained from our observation of the natural world. An observation of our field of experience will only take one so far. It is impossible for logic to breech the threshold into the eternal dimension of God. That requires the element of faith.
When Abraham acquiesced to offer Isaac, he did not conclude that God could raise Isaac from the dead based on any logical exercise. There is nothing in the world of man that could possibly lead Abraham to conclude through any logical process that someone could be raised from the dead to rejoin the living. Abraham had to look beyond logic to conclude the possibility of a resurrection. Logically, the facts are as follows:
Knife to the throat = an absolute outcome – death.
Fire to the flesh = absolute outcome – total destruction of the flesh.
These have always produced irreversible results – the death and total thermal consumption of the victim.
Abraham's experiences with offering sacrifices told him that sacrifices do not survive the ordeal; not ever! Human logic, based on human experience says, “If I do this my son will be irretrievably dead and gone.” Something was going to have to happen in Abraham's reasoning processes that would transcend the logic of the human experiential index. Abraham faced a logical dilemma - If Isaac is dead, how will the promise be fulfilled. This seems to create a contradiction between the promise and the command.
Abraham based his decision not on any logical assumptions, but upon the faithfulness of God. Abraham’s conclusion reached beyond the boundaries of applied logic – “God is able to raise one even from the dead.” This is certainly not a logical conclusion. How could Abraham possibly know this? He had no physical evidence to support such an extraordinary conclusion. The text never says that this knowledge was ever revealed to Abraham. He had never had a sacrifice get up off the altar and follow him home after the ordeal. He had had no experience with the dead being raised to life. The only thing Abraham’s experience could confirm to him about death was that logically, it is always decisive and irreversible. This is the limit of the logical approach. Abraham had to believe in something he could not see or otherwise prove empirically. But this was not blind faith. This was faith that was rooted in the revealed promise of God to make his descendants as numerous as the stars of the sky. Abraham came to understand that the realization of the promise was not dependent upon Isaac, whether he is dead or alive. The realization of the promise was dependent solely upon the will and the power of God. There were no other antecedent factors. The Hebrew writer confirms for us that faith was the only factor that drove Abraham’s conclusion and moved him to honor God's demand to sacrifice Isaac. The result of this was that God acknowledged Abraham as faithful, not logical.