My three non-Baha'i sources are below.
(1) Wikipedia
"The word
avatar does not appear in the Vedic literature,
[5] but appears in verb forms in post-Vedic literature, and as a noun particularly in the
Puranic literature after the 6th century CE.
Neither the
Vedas nor the
Principal Upanishads ever mention the word
avatar as a noun.
[5] The verb roots and form, such as
avatarana, do appear in ancient post-Vedic Hindu texts, but as 'action of descending', but not as an incarnated person (avatara).
[24] The related verb
avatarana is, states Paul Hacker, used with double meaning, one as action of the divine descending, another as "laying down the burden of man" suffering from the forces of evil.
[24].
The term is most commonly found in the context of the Hindu god
Vishnu.
[1][3] The earliest mention of Vishnu manifested in a human form to empower the good and fight against evil, uses other terms such as the word
sambhavāmi in verse 4.6 and the word
tanu in verse 9.11 of the
Bhagavad Gita,
[4] as well as other words such as
akriti and
rupa elsewhere.
[25] It is in medieval era texts, those composed after the sixth century CE, that the noun version of avatar appears, where it means embodiment of a deity.
[26] The idea proliferates thereafter, in the
Puranic stories for many deities, and with ideas such as
ansha-avatar or partial embodiments.
[4][1]"
(2) Sukdaven's "A systematic understanding of the evolution of Hindu deities in the development of the concept of avatara"
"An investigation into the development of the term avatara is well postulated by Bassuk (1987:3). He suggests that Sanskrit terms used to describe the manifestation of the descent of God into the realm of this world evolved from rupa (form, figure), vapus (having a beautiful form) and tanu (a living entity who accepted a material body) to pradurbhava (appearance). He claims that the Sanskrit word avatara gradually evolved from these terms and that this word is composed of two parts: the root verb tr meaning to pass or cross and ‘ava’ signifying down."
(3) Mary Brockington's "Helping the Cosmos: Indian Avatars":
"The [avatara] concept is not found in the earliest phases of Indic religion, where the systems now named 'Hinduism' had not yet emerged.2 Absent from Vedic thought, it begins to develop in the epics, the Rāmāyaṇa and the Mahābhārata, only in their very latest stages (from perhaps the third century AD onwards), and the word itself is not applied to the concept until considerably later (Brockington 1998: 277-89, 460-3; Brinkhaus 1993)."
Source?