Dhammapade verses 153 & 154 describe the enlightenment of Buddha Shakyamuni with the metaphor of collapsing a house. This house has been explained as standing for ego, self and name and form.
The historical event of the collapsing of the Tower of Babel (Babylon) happened at the time of Shakyamuni's enlightenment as its outer symbolic event. Therefore the timing of Siddhartha Gautama must be at the same time period as the collapsing of the Tower of Babel.
Theists want to remove Siddhartha Gautama away from everything that he has done, we don't have to accept this.
Naturally theistic traditions also give an entirely negative view of the Complete and Perfect Enlightenment that took place then. Buddha Gautama discovered a truly universal teaching, this the theists declared to be "confusion of tongues".
Time is a fluid factor, as Nagarjuna has said. This is concretely true, though difficult to perceive.
At the time of Siddhartha Gautama the Indus River civilisation (India) was in close contact with the culture of Babylonia. Zarathustrian sources mention a Magi Gaumata, (who was an opponent of Zoroastrians), this has been told recently in http://www.americanbuddhist.net
. The contact of buddhism with Babylonia and Persia is an age old controversy, tiring as such.