No, you are wrongly conflating the date ascribed to a version of a text (speculation based mostly on linguistic studies) with the events described in the text itself which predate it by aeons.

The Itihasas/Puranas talk about vast time scales populated by different beings with different lifespan lengths in a very specific and detailed manner. It contains both cosmic and civilizational histories all bound together in a single multi-branched narrative. Hence it is a very unique historical corpus from which much can be gleaned and mapped against modern studies.

Some resources:

Hindu units of time - https://en.wikipedia.org/wiki/Hindu_units_of_time

Yuga cycle - https://en.wikipedia.org/wiki/Yuga_cycle

As an example, The events in the Ramayana are dated towards the end of "Treta Yuga" but the text itself mentions a very long list of continuous lineage before coming to Rama. Look up "Treta Yuga" in the above pages and you can see how far back this particular narrative goes; you could calculate it as; "length of dvapara yuga + length of kali yuga to current date" and it comes to >800,000 years into the past!. Now add the lineages mentioned in the text itself and you go even longer into the past.

The interesting thing is that each of those timelines have some sort of Human/other beings in it!