It feels like one of those things in philosophy that religious people greatly exaggerate the importance of.
How you choose to "solve" it is up to you.
The solution computer scientists like a lot is coherentism. You pull yourself up by the bootstraps - like we do with self-hosting compilers.
Of course, it's just a conceptual game (like all philosophy). The idea of "prove to me that you know..." seems a bit like "Jump for me... Higher!"
(I personally am very aggressively areligious, so "faith" here does not necessarily refer to a spiritual faith.)
We need a much different concept than faith.
Faith means continuing to believe something that is massively contrary to the evidence, to preserve some type of fidelity or loyalty to a previous belief commitment.
I think this is massively different than acknowledging the fundamental deductive limitations of reasoning about epistemic metatruths.
You've just defined faith in a way that wins your argument, but that is not any kind of consensus definition of faith.
The ubiquitous notion of religious faith is similar to the second thing, and is not similar to the first thing. It’s not a matter of consensus or definition.
Appropriately named then!