Evidence or pramAna is required only when one wishes to prove something tangible, but not with respect to intangible issue.
Many intangible issues like LOVE, HATRED, JOY, JEALOUSY, etc, fall into the domain of ABSTRACT things. Their existence can be experienced but cannot be proved.
SPIRITUALITY is also an ABSTRACT thing. It can only be experienced.
Basically, the Veda talks about pure SPIRITUAL concepts, in an esoteric manner and is called Apaurusheya.
Apaurusheya does not indicate that they were not composed by humans. The Veda did come out from the mouth of a humans, albeit sages, like Atri, Viswamitra, Vasistha, etc.
However, the source of the Veda was is SELF REALISATION, a state of BLISS and it is DIVINE.
Sages like Atri, Viswamitra, Vasistha, etc, did not compose the mantras of the Veda, out of their thinking or scholarly wisdom.
Those mantras emanated out of SELF REALISATION, which is beyond human's comprehension. Those sages had spread that DIVINE wisdom to mankind in the form of mantras.