Greetings in that Divine and Most Precious Name of Our Lord and Savior Jesus Christ!
Simply put, all the religions are the same age, as they continue to perpetuate and transmit the same universal truths of the collective human experience and psyche, we all draw from the same well-spring of spiritual inspiration, much like with our linguistic diversity, we all are saying the same things in different manners and languages.
Read some Joseph Campbell and that should clear it up for you to be able to clearly see the interconnectedness of the one World Mono-Myth of heroes and saviors and avatars and God incarnate..
In regards to written codified forms of the original oral traditions, all religions, including those in India, began this same process around the 4th-9th centuries BC..
Further, the Indians have a trump card, their pantheon is an illusory manifestation of the Universal Monad, the One True God, by Divine Essence and Nature. For Indians, there is only a single Divine Nature (God) and It has appeared or manifested Its form in all India's (indeed, all the world's) religious traditions and histories so of course the logical inference is to claim India to have the oldest religions, but it is simply speculative aggrandizement.
We believe something similar in Christianity, but our avatar is different than theirs. In the Incarnation, the One True, Universal God became Incarnate in ONE single, permanent and eternal physical form, the Person of Jesus Christ.
That is our only real distinction between us and truly any other messianic or mystery religions, and further we aren't mutually exclusive, quite the opposite, we're mutually inclusive like Paul explained in Acts 17..