I have emunah in God. And yet, he doesn’t exist. Let me clarify.
What’s the common definition of existence? Something that has a tangible reality as defined by empiricism. God doesn't meet that criteria, at least not the contemporary idea of an incorporeal god. Through much of the early middle ages, Jews believed that God had a body.
But now, we believe Him to be intangible and incorporeal. So he doesn't exist.
That's why I think "belief" is such a poor translation of "emunah". I have emunah in Hashem. I feel that outside of the reality of our world there is a spiritual realm and it is in that spiritual realm that God is. I use "feel" because that's what it is. It's about an emotional connection, not an empirical one.
That's why I feel that those who try to "prove" God are on the wrong track. You can never prove God's existence, because by all standards of measurement that we use in our physical plane, God doesn't exist.