Are you talking about manifestations in real history or in stories that read like quasi-historical narratives? I'm not an expert on Hinduism, but Hindus seem to have told many stories about their gods that treat them like characters in history.

Below is a list of the avatars of gods in the Mahabharata, for example, an epic which is set in "the kingdom of Kurukshetra on the northern plains of India along the Ganges River."

Arjuna, for instance, is an avatar of Indra, and he interacts with the other characters in the narrative, on Earth. "Arjuna was the son of Kunti, the wife of Kuru King Pandu, and the god Indra, who fathered him due to Pandu's infertility" (wiki).

These avatars are just superheroes, as in legendary characters from history glorified in epic tales. The Romans did the same with their heroes, deifying them and singing their praises. Jesus is the same thing, except with the Jewish irony that he was a nobody, blown up to the proportions of a classical emperor or epic hero.

I doubt Hindu elites would be as confused as Christians about the difference between exoteric and esoteric interpretations of their myths.

https://en.wikipedia.org/wiki/Arjuna

https://en.wikipedia.org/wiki/Avatars_in_the_Mahabharata

https://www.encyclopedia.com/history/encyclopedias-almanacs-transcripts-and-maps/mahabharata