How are we to know that outside of pure faith?
I am not sure what “pure faith” is.
I don’t think anyone believes anything without good reasons, albeit, often VERY personal ones, that are not always amenable to explication in a mode that will be convincing to others.
When you say “to know” I suspect what you are getting at is, “Can we depict what we believe to be true, and the reasons for believing it, in a way that others will be likewise convinced?”
I am not sure that is a reasonable demand to make on oneself.
The challenge to enunciate any of our beliefs, even non-religious ones always faces us. There are many things that I know to be true that would be impossible to convince someone else about and many of these I would not even try because I, likewise know this fact, i.e., that some realities and truths defy objectification, also to be true. Of course, most of those would be personal and inherently subjective realities (internal “facts” if you wish) that are not susceptible to objective presentation without a corresponding loss of meaning and integrity.
Since many religious truths are personal ones, the danger is in convincing oneself that only those that can be “objectified” are worthy of assent. The reason that is a dangerous presupposition is because it assumes only quantifiable “facts” are valuable and important. Effectively, that would mean anything uniquely personal is valueless and unimportant.
For me, it is more important that I live and think to a standard of personal integrity than jettisoning much of what is meaningful and valuable for the sake of demonstration or objectification. “If it can’t be objectively demonstrated it can’t be true,” is a ridiculous notion that presumes personhood is meaningless and illusory.
I don’t deny some beliefs can and should be demonstrated publicly, I merely deny that all beliefs or “internal facts” can or should be. There are “internal” means by which beliefs and one’s own internal integrity can be weighed and assessed which need not and, indeed, should not be subjected to objective methods for quantification or verification.
The important thing, as far as maintaining personal integrity is concerned, is to recognize the difference. Eliminative materialists and many atheists seem to have lost the capacity to recognize the difference and presume that “knowledge” is simply reduced to what can be objectified and demonstrated - a very shallow view of existence, truth and reality.
It is like holding that any written material should be taken at face value. That an author would not “write into” the text any more than what appears literally on the page, so “reading into” text or reading “between the lines” is forbidden, no matter how cogent or meaningful such a rendering is. Even when the literal meaning pales, falters or cannot explain the rest of the text.
If we begin with the same presupposition - that all truth is literal and “objectively” present - we have effectively conceded that to “know” something is essentially identical to demonstrating it and the content of knowledge becomes reduced to and identical with the demonstrable object (the “text”) itself.
So your question (How are we to know that outside of pure faith?) would seem to be asking - if by to “know” you mean “demonstrate” - is: "How are we to demonstrate THAT to anyone who thinks “TRUTH,” by definition, means only that which is amenable to objective demonstration?
Perhaps by convincing them that no one truly lives by that belief, otherwise they would simply toss everything they “know” to be true about themselves. As Socrates would observe, “The unexamined life is not worth living.” A move to accept only demonstrable facts would effectively make everything about every “self” unexaminable and, hence, according to Socrates, at least, EVERY life not worth living.