The late Vedic period (time of the Upaniṣads) brings up to the time of the historical Buddha (6th-5th centuries BCE).
Thus it is not an accident that the Upaniṣads and early Buddhist philosophy share some basic perspectives on our existence.
Both Upaniṣadic Hinduism and early Buddhism are interested in perceiving reality as it actually is by delving beneath the everyday world, to which our attachment causes rebirth in endless lifetimes.
Ultimately, one who follows this kind of introspection can attain a state of realization that transcends rebirth.