False, the Vedas are specifically and historically dated to no older than ~300 -200 BCE.
Bhagavad Gita - Wikipedia.
According to Arthur Basham, the context of the
Bhagavad Gita suggests that it was composed in an era when the
ethics of war were being questioned and renunciation to monastic life was becoming popular.
[46] Such an era emerged after the rise of
Buddhism and
Jainism in the 5th century BCE, and particularly after the semi-legendary life of
Ashoka in 3rd century BCE. Thus, the first version of the
Bhagavad Gita may have been composed in or after the 3rd century BCE.
[46]
Linguistically, the
Bhagavad Gita is in
classical Sanskrit of the early variety, states the
Gita scholar
Winthrop Sargeant.
[47] The text has occasional pre-classical elements of the Sanskrit language, such as the
aorist and the prohibitive
mā instead of the expected
na (not) of classical Sanskrit.
[47] This suggests that the text was composed after the
Pāṇini era, but before the long compounds of classical Sanskrit became the norm. This would date the text as transmitted by the
oral tradition to the later centuries of the 1st-millennium BCE, and the first written version probably to the 2nd or 3rd century CE.
[47][48]
According to Jeaneane Fowler, "the dating of the
Gita varies considerably" and depends in part on whether one accepts it to be a part of the early versions of the
Mahabharata, or a text that was inserted into the epic at a later date.
[49] The earliest "surviving" components therefore are believed to be no older than the earliest "external" references we have to the
Mahabharata epic. The
Mahabharata – the world's longest poem – is itself a text that was likely written and compiled over several hundred years, one dated between "400 BCE or little earlier, and 2nd century CE, though some claim a few parts can be put as late as 400 CE", states Fowler. The dating of the
Gita is thus dependent on the uncertain dating of the
Mahabharata. The actual dates of composition of the
Gita remain unresolved.
[49] While the year and century is uncertain, states
Richard Davis,
[50] the internal evidence in the text dates the origin of the
Gita discourse to the Hindu lunar month of
Margashirsha (also called
Agrahayana, generally December or January of the Gregorian calendar).