To be logical, Hinduism should have been the first as there is no trace / evidence for its initiation. But Buddhism, everybody knows that the followers of Gauthama Budha are 'Buddhist'. Buddha lived and taught in the northeastern Indian subcontinent some time between the 6th and 4th centuries BCE.

It cannot be told, that the existence of the Hinduism is unbelievable (as answered by the previous user - answer edited) just because there is no trace of initiation of the Religion. There are evidence for existence of the religion in history.