In academic fields, particularly in science, practitioners are often careful to to say they have confidence in something rather than saying they believe in it. Example: "I am confident the theory of evolution" instead of "I believe in they theory of evolution". This distinction is important, because having confidence imputes having a body of evidence that leads the speaker to find the idea probable; belief implies having faith, which requires no such evidence, and no empirical means to estimate how likely the idea is or not.
In Japanese, it seems that 確信する is the closest means of communicating "to have confidence in". But this phrasing uses 信, which means faith or belief, and has strong (?) religious connotations. Canvassing Japanese L1 speakers I've found no way to avoid using 信 and no way to avoid communicating some degree of (blind) faith.
So my question is: Is this (pedantic) degree of precision possible in Japanese? Is anyone aware of examples where this distinction is made?
Corollary: Am I mistaken in associating 確信する with 信じる?