Ultimately all claims of antiquity must be decided by evidences.  One of the prime evidence evidently should come from Archealogy  and Art.

The oldest archealogical cave ever discovered and recorded  in India is Prehistoric Rock Art at Bhimbetka

 

The "caves"  are actually, deep overhangs  in Bhimbetka, near Bhopal in Madhya Pradesh.  These caves are decorated with art in the usual neolithinc art form which are dated around 8000 BC and continuing in some caves into historic times. These caves depicts animals and do not represent any gods  The people essentialy were hunters.

 

These later caves includes horses as a means of transport and is dated second millenium roughly the time of early Aryan migration

 

The Ajantha Ellora Caves of Maharashtra  were essentially Buddhist Monasteries built between the 2d century BC and the 5th century AD

 

Sadashiva Murthy in the Elephanta Caves off Bombay with its three faces - Tatpurusha-Mahadeva (center), Vamadeva-Uma (feminine - right side), Aghora-Bhairava (Masculine Fierce - left side) is heavily reminiscent of Hebrew Kabballa. These are dated at Satavahana  period between  2d century BC - 3d century AD

 

This inscribed Garuda column, in Besnagar near Udayagiri, was erected in honor of Vasudeva  by a person named Heliodorus, who was a Bactro-Greek envoy from Gandhara to the court of Vidisha. This column was built in 113 BC. Most people try to equate Vasudeva as Vishnu. Garuda is considered to be the vehicle of Vishnu.

Sanchi Buddhist Stupa was erected by Ashoka Maurya in the middle of the 3d century BC

 

This north gate portrays some scenes from the life of Buddha.

The earliest direct portrayal of hinduism is found in the following lingam:

 

Shiva Linga Gupta, Early 5th century AD Udayagiri, Madhya Pradesh, India.

This type of linga is known as ekamukha (one-faced). In the rock-cut caves at Udayagiri Shiva  is worshipped inside, and  Vishnu is worshippped outside

 

Varahavatara is found in one of the caves where Nagaraja is seen submitting to Varaha.

 

South Indian culture seem to take shape much later,  King Rajasimha, of the Pallava dynasty, built this Shiva temple in the early 8th century

 

These 7th century shrines  were carved during the reign of King Mamalla (Narasimhavarman I, c. 630 - 670 A.D.), after whom the site is named. Each temple is a monolith, carved whole from an outcropping  rock.

If we care to look into the art and architecture of Indian mythology and temples, we will be surprised at the lack of any temples  prior to AD 200 dedicated to any of the gods or avatars.  Even though Indian culture dates back to 8000 BC. the Hindu culture as envisioned today did not exist far beyond the first century AD.