One might respond to Russell in many ways. One might say that we do have good evidence of God's existence. One might say that God, if real, is so radically unlike a teapot that to assume we must come to know them in the same way is deeply mistaken. I have some sympathy for both responses. (Of the two, the second seems closer to the heart of the matter.) But to me they've always seemed to fall short of the mark.
The issue is this: the God-hypothesis would have us assume that God is an object that stands outside us and whose existence can be known only by inference from what is clear either to sense or to intellect. I reject this assumption.
I am not alone in this. Much Christian theology rejects it. God, we are told, is He in whom we have our being. We are with Him, but not as two who stand side by side. We are through Him, and Him through us. Thus we are not ours alone. God is in us, and at every moment He sustains us. Every iota of what is good in us - and all that truly is is good - is Him. When conscience speaks, it is the voice of God. When we love, the love we share is God.
God is not over and above. (Perhaps we should say that God is not over and above only, for though in us He is no exhausted by his presence in us. We are finite, He infinite.) Rather He is within, and thus is to be found within.
Thus God is not to be discovered as the teapot would be discovered if in fact it were there. The believers relation to God is not that of knower to an external object known. This is why I find atheism a bit ridiculous. I've had a number of moments in my life where the presence of God within me has become quite clear. Even now as I sit with the noise of traffic around me, cold and alone, and still feel that presence. It is a hint, a whisper. It is as motion caught in the corner of the eye. Attention is mostly elsewhere, but a fraction is upon it, and I know that He is there.
When someone tells me there is no God, it seems to as if I have been told that there is no sun or moon. Perhaps I do not see them now, or see them only faintly. But I know they are there.
Perhaps it would be better to say that it seems to me as if I have been told that I have never felt love, or regret. Of course I have, I would reply. I feel them now. They are here before me, with me. I cannot doubt them. S0 too I cannot doubt that God exists. He is here with me now.
So I say to the atheist: God is within you (and without you too in all creation). Do you feel the tug of conscience? That is God. Do you love someone? That is God.
Do not ask me then to marshal evidence in favor of God as He were some variety of exotic particle that could be made to show itself were conditions just so. Do no demand miracles. Do not demand proofs. Search yourself. There is within you a power upon which you depend, a power upon which all depend. Do not close your eyes to it.