I'd argue that it can't be.
The argument would go something like this. Suppose we found some non-scientific method of gaining knowledge about some subject, let's call it an "oracle". Of course, for it to really have found this method, for us to use it, and for it to "surpass" what we presently have, we have to know that that's what we've found. How would we know, then, that the oracle was a valid method of gaining knowledge at all? Well, we'd have to test it against reality to see if it works. But once we've done that, and found that it works, then the oracle is a scientific instrument, it has been validated by the scientific method, and the fact that it works is a scientific fact. The oracle would just be another thing like a thermometer or a spectrometer that we've shown can be used to find stuff out.
I'm not so sure. Just as Science bootstrapped itself, I don't see why there couldn't be a new method that could work completely independently. I think your insistence on verification by science is a symptom of our lack of any known alternative method.