Introspectively, it seems clear to me that it is possible to choose to have faith. It might be, though, that what this "faith" is is a more complicated question than it would initially seem to be. But I can clearly imagine adopting something that very much feels and would seem to work like "faith".
(Might as well now mention that I've been an atheist all my life, and still am. I don't currently have any faith I know of, except perhaps the thing about a time-continuous self.)
I "chose to have faith" when I had a crisis of faith as a kid. However, after my crisis of faith I no longer actually made predictions based on my faith-beliefs.
"Choosing faith" and actually believing something are very different.
What must a sane person1 think regarding religion? The naive first approximation is "religion is crap". But let's consider the following:
Humans are imperfectly rational creatures. Our faults include not being psychologically able to maximally operate according to our values. We can e.g. suffer from burn-out if we try to push ourselves too hard.
It is thus important for us to consider, what psychological habits and choices contribute to our being able to work as diligently for our values as we want to (while being mentally healthy). It is a theoretical possibility, a hypothesis that could be experimentally studied, that the optimal2 psychological choices include embracing some form of Faith, i.e. beliefs not resting on logical proof or material evidence.
In other words, it could be that our values mean that Occam's Razor should be rejected (in some cases), since embracing Occam's Razor might mean that we miss out on opportunities to manipulate ourselves psychologically into being more what we want to be.
To a person aware of The Simulation Argument, the above suggests interesting corollaries:
1: Actually, what I've written here assumes we are talking about humans. Persons-in-general may be psychologically different, and theoretically capable of perfect rationality.
2: At least for some individuals, not necessarily all.