Inquiry and innocent faith in the work of God

Hello Rabbi,
I wanted to ask what, in your opinion, is the place of innocent faith and what is the place of investigation in the service of God. Should we proceed only through intellectual investigation or is there also room for unfounded faith? Is it even possible to proceed only through intellectual investigation? After all, we have seen that, no matter how much we want it to be – the analytical is empty. In other words, even if we are rational people, we need axioms to apply the principles of logic to – and it seems to say that this is where innocent and unfounded faith comes in, right? (As far as I understand, the definition of axioms is that they are unfounded..)
In addition to your opinion, I would be happy if the rabbi could elaborate on what the sages of the ages seemed to think. I understood that this was a Rishonim dispute, but I was unable to get into its details. Are there Rishonim who are at different extremes? That is, who really think that it is possible only through intellectual investigation or only through innocent faith without investigation? Or are they all talking about a certain spectrum? Of course, there is no need for a full review of the opinions of the Rishonim now, but I will explore two or three key positions on the issue if that is not too much.
Thank you very much!