"I can think of two yes or no answers just off the top of my head"

"Truly, you are a God who hides himself." said Isaiah (45:15)

Why?! If there is a God, why does He not make Himself more obvious? Think how much simpler it would all be if there was a yes/no answer that was universally evident.

Dallas Willard posits that the hiddenness of God allows people to define themselves:

And why would God hide himself? Because God loves us, he wants to be known to us. That is the way of love. But because we, in our rebellion against him, are hardened in our insistence on having our own "kingdom," he must hide from us to allow us to hide from him and to pretend we, individually and corporately, are in charge of our life. He is such a great and magnificent being that, if he did not hide from us, we could not hide from him. He allows us the pretense of being our own god because that is what we want, what we choose. Pushed to the limit, this choice results in the terrible evils of which we have proven capable. (From 'The Craftiness of Christ', Dallas Willard)

I quite like this answer. But I suspect it is more palatable 'from the inside'...that is, it makes a lot of sense to someone who feels they already know something of a God who fits this description, but it doesn't necessary persuade someone who has had no such experience.

Belief in God may not be provable, but that doesn't mean that it is not evidence based. In particular, the Christian faith makes remarkable truth claims which, whilst not scientifically testable, can nevertheless be evaluated by scrutiny and rational investigation. The person, teaching, life, death and resurrection of Jesus is recorded in history and those accounts can be examined and assessed for veracity and integrity. The Bible as a whole weaves a remarkable narrative*, written over the course of (up to) 1,500 years by as many as 40 different authors, of God's interaction with and plans for humanity, which (to many readers) resonates with insight and timeless relevance. And the transformed lives and testimonies of those individuals who claim to have experienced a personal relationship with God can also be considered as evidence to be weighed up in the search for truth.**

I'm not presenting this as a 'done-and-dusted' argument for belief in God...more of the beginnings of a counter-example to the claim that we've 'nothing to go on'; God is 'hidden'...but not invisible to those who dare to seek Him with an open heart and mind...

And so to one of my favourite bits in the New Testament, which has Paul talking to a bunch of Greek scholar-types (the Areopagus, apparently, was some sort of aristocratic council):

So Paul, standing in the midst of the Areopagus, said: “Men of Athens, I perceive that in every way you are very religious. For as I passed along and observed the objects of your worship, I found also an altar with this inscription, ‘To the unknown god.’ What therefore you worship as unknown, this I proclaim to you. The God who made the world and everything in it, being Lord of heaven and earth, does not live in temples made by man, nor is he served by human hands, as though he needed anything, since he himself gives to all mankind life and breath and everything. And he made from one man every nation of mankind to live on all the face of the earth, having determined allotted periods and the boundaries of their dwelling place, that they should seek God, and perhaps feel their way toward him and find him. Yet he is actually not far from each one of us, for

   “‘In him we live and move and have our being’;
   as even some of your own poets have said,
   “‘For we are indeed his offspring.’ 

(Acts 17:22-29)

* That's not to say that it's all narration in style -- I find it fascinating that it's made up of so many different types of literature: history, poetry, law, prophecy, parable, correspondence...

** If you don't think you know anyone whose life bears possible evidence of God's grace at work, ask me about the last 10 years or so in particular of mine :-)