The person who asks for evidence is not necessarily asking to dismiss the experience.

Questions about proof and questions about belief get tangled together, especially when the subject is personal. Someone asking how you know, or what the source was, may be trying to understand the situation well enough to help, not signaling that they think you are wrong. The request feels like doubt because it arrives at a moment when you needed agreement first. Both things can be true: the experience is real and the details still matter.

If you are asked for evidence, check whether the person is doubting you or simply working. If you are the asker, say you believe them before you ask anything else.