Why was buddhism able to make such inroads among the indian people at a time when brahmanical beliefs had long been dominant in the subcontinent?

Because of Egalitarianism, the belief that conveys any human being could aspire to Nirvana. This belief conveys that as long as they followed the Buddha's teachings and abandoned all of their worldly desires, they will be free from the set of reincarnations and eventually entered the Nirvana