It depends on how compelling the evidence is, and how verifiable it is. I don't think the speed to which you change your mind matters, it's just that you are open-minded enough to change your mind. If you hold a strong belief and someone gives compelling evidence that makes you pause on your strong belief, then that in and of itself is enough.

You don't have to go hook line and sinker at the very first piece of evidence, because it's the preponderance of evidence that changes minds. The very first experiment that showed the duality of light didn't immediately change people's minds, but it broke the seal, and the accumulation of evidence did afterwards.