God could look like a baby with a moustache
In the Bible, there is not a word about God's appearance. As a consequence, the Christian God could look like anything: a white star, a mountain in Egypt, a majestic tree, a cow, an Asian woman or a baby with a moustache. Or even an old muddy boot. Yet, every Christian would tell you that He does not look like an old muddy boot, but more like an old man with greyish beard and long hair. Definitively Santa Claus with a white toga. So if not in the Bible, where does that image come from?
It seems to me that painters may have shaped God's believed appearance in Christianity, therefore that visual cognition shaped a naive concept of God. Can it be true?
How is God first represented in paintings?
I expected to find an easy answer but I did not. During the Roman Empire and after, holy characters are very often depicted in icons (religious works of art). The Church encourages to depict holy material and it is extremely trendy to have an image of a Saint or a piece of its remains. While Christ is abundantly represented, I could not find a single icon of God before the 15th century.
Icons of God may have been lost during the 8th century. In 726, a volcano near Santorini discharges deadly tsunamis on Byzantine Empire. For Leo III, the emperor in charge, the cause is clear: they made God angry in worshiping thousands of icons. Inspired by the Muslim soldiers who cumulate successful battles after forbidding any sacred image and even more, Leo conducts the first iconoclast: literally the "image-breaking", an edict forcing people to destroy all icons.
However, on the western side, the situation is opposite: the Pope condemnes Leo III, he confiscates some of his villas in the West and continues to welcome icons. West and East jointly agree on that question with the Second Council of Nicaea in 787 but only for a short time until Leo V decides the second iconoclast in 814.
So why can we not find Western icons of God? Well, what applied to sacred characters does not apply directly to God. To catch that, listen to St. John of Damascus, that was yet a strong opponent to Leo's iconoclast:
"If we attempt to make an image of the invisible God, this would be sinful indeed. It is impossible to portray one who is without body: invisible, uncircumscribed and without form."
- following a successful career, painting somewhat boring sacred icons;
- trying to depict God: meaning taking the risk of improperly depicting God. Remember that blaspheming against the Holy Spirit is the only unforgivable sin  according to New Testament. You may be properly banned, perhaps executed and your soul might be damned forever.
Because Christ is the incarnation of the invisible God, Christ is then the favoured way of representing God. It ended up in God weirdly shown as Christ's twin brother (see below)...
For the Trinity to be complete, the Holy Spirit is often added, almost always shown by a white dove, sometimes by adding a third twin, like on the Dogmatic Sarcophagus!
Then, Christ was represented as old: a concept called "Christ of Apocalypse". An amazing one is this Christ of Apocalypse made by da Milano in 1364 (You can admire it at the National Gallery in London - see on the left).
God was also partially revealed by timidly painting his hand, but anonymously, like in the two following works of art (I also put a later beautiful Verrocchio). It is a human hand: how will be the rest of the body?
What is the first painting of God's body?
For the moment, the older painting I found where you can see the full God, is the Trinity from Barnaba da Modena, in 1374.
God is depicted as a hairy old guy and he is helping the Christ in his painful crucifixion. He is wearing a blue coat with golden lines with a orange top.
The painting is the second part of a 4-part painting that appeared in a Spanish cathedral. The four animals are actually representations of the four gospel writers - demonstrating that God could have been represented as an animal here.
I found it randomly in the National Gallery and it is more impressive for real. There is not much to say about Da Modena, except perhaps that it seems that this painting was one of the last ones he did.
The next one is the Pietà from the gothic Dutch artist Jean Malouel, in 1405 (see on the right). God looks like a hairy old man while he holds his dying son. It is clearly God because you can see the dove of the Holy Spirit just between them, to complete the Trinity. The painting can be seen in the Louvre and is more impressive in reality.
Jean Malouel was an important painter in France at that time, protected by the court of Burgundy. Strangely, the painting is more well-known for being the first circular painting (tondo) than for being one of the first representations of God.
However, Jean has two nephews: the Limburg brothers. The brothers probably created the 3rd and 4th images of God in 1411, with two illuminations of the fantastic "Très Riches Heures du Duc de Berry" (below). On the first, you can see God quietly chatting in the Garden of Eden. On the second, God is quietly conducting a solar chariot (detail on the right).
I think the brothers just followed their eminent uncle's example in representing God similarly: a quiet old man with long hair and long white beard. I don't know how the Pieta was appreciated but the Duke of Berry was extremely happy about the brothers' illuminations.
Nonetheless, it is crazy courageous of them to dare depicting God in those times.
After that, Renaissance in France starts up and the court of Burgundy actively leads it. All images of God will follow the same model with, at its apogee, Michelangelo's well-known painting below. Yet, all of this does not explain why God is painted that way on the first time.
Why God's first image is the one of an old man?
Interestingly, Adam Lewis commented below that it could come from a short description in Daniel 7:9, a jewish biblical apocrypha (i.e. unofficial text):
"I beheld till the thrones were cast down, and the Ancient of days did sit, whose garment was white as snow, and the hair of his head like the pure wool: his throne was like the fiery flame, and his wheels as burning fire."
Maybe you know that Jewish and Christian churches believe in a hierarchy of angels, in which the more powerful (the Cherubs and Seraphims, always next to God) are systematically depicted as babies. The less powerful angels, like the archangels are usually depicted as older men. So if you follow that logic, God should be shown as younger than a baby...
A better choice nowadays seems to be a woman: according to a psychology study , the mother conceptual image fits more God's image than the father image. Personally, I would have gone for a pretty cool cosmic giant turtle with four elephants on its back.
Painters received the burden of painting the Invisible (God) but they did not even try to suggest that invisibility. It is perhaps because we are not sure that God is really invisible. He is, according to Gospels  but Jacob and Moses have seen God in the Old Testament ...he could be kind of transparent. Using transparency seems a satisfying solution to that inconsistency, as do adepts of the Invisible Pink Unicorn in their sacred symbol. The parody religion mocks religious nonsenses, when God is supposed to be something and its opposite. The Unicorn is then paradoxically pink and invisible.
Finally, how do we know that some painters did not paint God as a tree or an old muddy boot? We can tell that Malouel did represent God in the Pieta because its representation fits our visual expectation of God. In the beginning of the text, I was wondering whether our visual expectations come from paintings and shape our concept of God. It may be simply the opposite, that our (simplified) concept of God shapes our visual expectations and biases our interpretations of the presence of God in paintings.
PS: if you know older representation of God, please tell me!
 Tamayo, A & Dugasa, A (1977) Conceptual Representation of Mother, Father, and God According to Sex and Field of Study. The Journal of Psychology: Interdisciplinary and Applied. 97:1.
 "No man has seen God at any time; the only begotten God, who is in the bosom of the Father, He has explained Him." (John 1:18).
 "So Jacob named the place Peniel, for he said, I have seen God face to face, yet my life has been preserved” (Genesis 32:30).
 "Thus the Lord used to speak to Moses face to face, just as a man speaks to his friend". (Exodus 33:11).
 The name of that sin is a bit misleading given that pretty everything enters into the blaspheming-against-the-Holy-Spirit category, like not believing in the Holy Spirit or asking for his forgiveness without really feeling sorry for your faults.