1. As with, say, colour perception, reports on the direct experience of feelings are necessarily veridical. E.g., you cannot report (in good faith) that you are experiencing fear, while not in fact being afraid.
2. This experience reveals that fear is real. One needn't go looking for fear in the world, as one would go looking for bigfoot or quarks. This is just not what we have in mind when we attribute reality to certain things.
3. I experience love.
4. God is, by definition, love.
5. Therefore, God is real.
Issue will be taken, of course, with step 4, as having a stipulative character. I am taking it from 1 John 4:8, but others will look to other biblical passages and to other religious traditions to say that God is an anthropomorphized being of some sort, or a theriomorphized one, or a many-headed chimera: in any case, a conscious agent, not a feeling.
But here one might also note that any virtue or feeling at all can be, and often is, anthropomorphized: justice, beauty, purity, etc., have all been represented as human beings in the history of art, and a future historian or a Martian anthropologist would be forgiven for inferring, for example, that late-modern New Yorker-New Jerseyans follow a cult around the goddess of liberty. This is one of the central concerns of the Jean Seznec's great book of 1940, The Survival of the Pagan Gods: the Mythological Tradition and Its Place in Renaissance Humanism and Art. We cannot make a facile distinction between the polytheism of the ancients and the artistic symbolism of the Renaissance: we often don't even know of ourselves whether we have in mind a concrete being, or rather an abstract ideal, principle, or emotion represented in the figure of a concrete being.
So I take it that in the Gospel of John what we are seeing is a stripping away of the symbolic dimensions of the social experience of God in order to lay bare the truth of the personal experience of God. And what we are left with is a sort of proof that is, in its own way, as forceful and incontrovertible as G. E. Moore's "Here is a hand, here is another hand..." It says, to distill the five steps down to the basic inference at their core: "Here is love, here is God..."