Brahman isnt really a non entity. As a monadic, transcendental, universal principle, it isnt empty, zero or a void, but infinite, absolute and all-full. As per Advaita(and also Mahayana Buddhism), it isn't Brahman/Nirvana thats the non entity, but rather the physical universe(Maya/Sunyata) in comparison to Brahman. Brahman is said to be absolutely existent, as opposed to Maya which is relatively existent and ever changing.
Brahman is necessary to explain how the mind becomes conscious, and to explain further where the soul comes from, where it goes after liberation and what its nature is.
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Ironic that I can use your own reply to rebut your reply.