Is there any evidence for believing in Hashem & Judaism other than faith?
It depends on one's starting point. Someone who was raised in a secular humanist household and whose identity is invested in secular humanism will undoubtedly see no reason at all to accept any sort of higher being or revelation.
On the other side of the coin are many of us who are starting from a point of faith in God and faith in Torah MiSinai.
We don't have this faith because we have deduced it from logical processes. Rather, we feel it deeply, in a way that is not subject to logic or rationalism. It's a different kind of belief, not based on empirical evidence. We simply KNOW.
Being intelligent individuals raised on modern western rationalism, we confront evidence that the Torah is not what traditional Judaism claims it to be.
What do we do? Rather than throw out all of our deeply held beliefs, we must modify them to fit the empirical evidence.
That is, emunah still has a place in our thoughts and hearts. It's still the place where we start from. We simply must adapt aspects of our belief to the incontrovertible evidence that we are faced with.
I don't claim to speak for everyone who comments and posts on this and like minded blogs. But I think most think as I do.
Coming from a firm belief in God, I see no need to jettison that belief. There is nothing in the documentary hypothesis to force me to reject God's existence.
The traditional views about the text of the Torah are another thing. I cannot, based on what modern scholarship presents me with, accept that the exact text of the Torah, word for word, was given to Moshe at Har Sinai.
Does that mean I must accept the conclusions of the DH? Certainly not. Much of the DH is simply intelligent speculation. The evidence requires me to modify my thinking somewhat. But it doesn't in any way prove the nonexistence of God or that no part of the Torah has its source in divine revelation.
I guess in the end part of it does come down to blind faith. But if we were only interested in what can be proven by logic, then this topic wouldn’t be so popular in the blogosphere.