Do we have any details about the oldest idol of any Hindu God found anywhere in the world?
Before the Kali Yuga, idols were few and far between, because the Archa form of gods hadn't really been established yet. Still, there are many idols that date back to the periods of the Ramayana and Mahabharata. But there are other idols even older than those. Here are three contenders for the oldest idol:
As I discuss in this answer, the Shiva Purana relates a famous story about a contest that Brahma and Vishnu had, in which they raced to the top and bottom of a pillar of fire that Shiva had turned into. It's unclear when this contest took place; the Shiva Purana suggests that it happened close to the time of creation, but there's reason to believe that the account found in the Shiva Purana is a later interpolation. There are also claims that the story is old enough to be mentioned in the Brahmanas of the Rig Veda, but as I discuss in this question, I haven't been able to find such a mention.
Regardless of when the contest took place, it's clear where it took place: the Arunachala hill in the town of Tiruvannamalai in Tamil Nadu. After the contest was over, Shiva transformed his form as a pillar of fire into a Shiva Linga, the famous Arunachaleshwara Lingam, which you can see here:
Note that this isn't the only occasion where Shiva appeared as a pillar of light; he appeared in 12 other places, the sites of the famous Jyotirlingas, for instance the Tryambakeshwara linga whose story I discuss in my answer here. You can see pictures of all 12 Jyotirlingas here, but I think those appearances of Shiva all happened after his appearance in Arunachala.
Most people only know the story of Vishnu's incarnation as Varaha the boar up to the part where he defeats the demon Hiranyaksha and rescues the earth from the water. But as I discuss in this answer, afterwards he came down and started living on the Earth for the benefit of his devotees, and in fact Varaha is still alive to this day, on the western bank of the Swamipushkarini lake near Tirupati. (In fact the original name of the Tirupati area is Adi Varaha Kshetra - the place of the first Varaha.) Devotees of the Tirumala Venkateshwara Temple in Tirupati, located on the southern bank of Swamipushkarini, are supposed to first worship Varaha in the western bank.
In any case, since Varaha lives in that area, there is a temple for him on the western bank, the great Varaha Swami temple, and it contains a Swayambhu (divinely created) statue of Varaha:
Now Vishnu's incarnation as Varaha happened at the beginning of the Kalpa; in fact that is why the present Kalpa is called Shwetavaraha Kalpa, or the Kalpa of white Varaha. So this idol is certainly one of the oldest idols.
Now we come to what I think is the real oldest idol in existence. Shortly after the birth of Brahma, which I discuss in this answer, Brahma started praying to Vishnu (perhaps with the hymn Purushagati, as I discuss here). As a result, Vishnu appeared before him and gave Brahma a divine statue of Vishnu lying down on the serpent Adiseshan. Much later, Surya the sun god began to worship it, and then Surya's grandson Ikshvaku had the statue brought to Ayodhya so that he could continue worship it. The statue was passed down through the kings of Ayodhya, until it came to the possession of Rama. Rama gave it to Ravana's brother Vibhishana, who planned to install it in Lanka. But on his journey from Ayodhya to Lanka, Vibhishana put the statue down in the island of Sri Rangam in the middle of the Kaveri river, so that he could bathe in the holy Kaveri. When he came back, he found that he could not pick up the statue with all his might - Vishnu wanted to stay in Sri Rangam.
This statue is the idol of the famous Ranaganatha temple in Sri Rangam:
Considering that it was worshipped by Brahma from the time he was born, Ranganatha is probably the oldest statue on Earth.
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