"Evidence " means physical evidence, I guess. The paradox is this - are there non-physical phenomena for which there is physical evidence?
Is there evidence for Out-of-body experiences? If you never had one, you would say no. However, try to guess the answer before jumping here :-)
Can we do a thought experiment? Nuclear war, Solar flares, green house effect, whatever. Humanity has gone blind. Lost the sense of sight.
Thus shapes, colours, forms, changes of state of these properties etc cannot be perceived. They do not see clouds, the blue sky, the far-away stars, birds flying silently in the sky, distant blue seas, lush green forests and so on. Undoubtedly a greatly diminished life, compared to people like us.
Now, if one or two of them acquire eyes somehow, a whole new world opens up. They start experiencing and describing things that seem incredible to other people. They may be considered to have too much imagination, or even mad. They may eventually be persecuted or thrown out of the human community.
The history of science itself has plenty of these happenings. Until radio waves were discovered, Science did not know of its existence, though radio waves have existed for all time. This example extends to x-rays, gamma radiation and many other phenomena discovered at some point in time.
If due to some future catastrophes, suddenly the faculty of colour is lost, then Science will gradually start to deny the existence of colour. If people with long memories, or memories of their ancestors’ tales, talk about these things, they will be considered superstitious.
Update: (@Josh) - Another thought experiment. A 2-dimensional being cannot fathom that things are happening in a 3-dimensional world. Any physical phenmenon will appear to arise from other physical phenomena in 2 dimensions. Similarly, things coming from a 4th dimension will appear to be happening in the 3-dimensional world that appears to our senses.
The fourth dimension theories of Hinton and Ouspensky have a thorough treatment of the subject.