You can't have proof in the sense that you can prove "2+2=4". If the existence of God were to be written in flaming letters in the sky, where's your freewill? If incarnation has any value, it's surely to enable us to learn and develop, and we couldn't do that with God obviously looking over our shoulders, as it were. Like parents with their children, he has to give us some space.
Gordian Knot misses the point. Firstly, we don't have to say "which God". If we are talking about the supreme being, then there can only be one. Statements about the precise nature of that being are, of course, another question, but deciding about the existence of God obviously precedes deciding whether that being is better described as the Trinity or Vishnu. As for the sort of evidence demanded, we know many things without "Solid … evidence … through multiple separate tests". Try proving that you love someone in that way! And how do you apply repeated tests to, say, an historical event? If you define evidence as the sort used in physics, then naturally all you are going to accept is the sort of material dealt with by physics.
We have two types of evidence. religious experience and philosophical argument. The latter can show that God is probable, but the fact that something could probably exist is naturally no proof that it does. But such arguments can underpin those from religious experience: they can show that the concept of God is coherent and so reports of religious experiences can't just be classed with hallucinations, as Dawkins does. And if you read reports of mystical experiences, they are consistent. One can find the same sort of experiences reported from all over the world and throughout history.
