How do you know that scientific knowledge is the only valid kind of knowledge?
Well, you don't. That is a value judgment (an irrational one, at that) for which no one scientific evidence exists.
One can, of course, formulate positivism differently: "scientific knowledge is the best kind of knowledge." The abovementioned problem remains, but it's less fatal. But that raises the question of how "best" is to be understood.
There are plenty of things we know to be true for which no scientific evidence does (or even can) exist. Scientific evidence is, in some ways, based on them. Mathematical axioms are a good example. You can't prove that for every two points in space there is exactly one straight line connecting them. You just accept the self-evident truth of it.
But once you do that, you're moving away from positivism. You acknowledge that scientific knowledge is, ultimately, only useful for those phenomena which science is intended to study: naturalistic and materialistic phenomena. And when you grant that, it's a short leap to assert that science necessarily has nothing to say about non-naturalistic and non-materialistic phenomena: the substance of miracles and the existence of the divine.
None of this is new, of course. But I sometimes wonder that it has to be said. I have a cold and I'm sleep-deprived, yet typing out this criticism took me all of five minutes and I engaged, like, four neurons.