The parentage of Brahmi is somewhat problematic thus judgement should be left up to the reader as to whether the language is of Aramaic, and thus Semitic, or Indus origin.
The earliest uses of this script are from the Buddhist inscriptions known as the Ashoka edicts from the 3rd century CE. In his work, The Origin of the Brahmi and Tami scripts, Righter (1993) asserts that, the language of the edicts is mostly Prakrit or Pali, and ... it is more likely that the Buddhist King made only use of an invention that was already known for several centuries (320.)“
Rodgers (2005) agrees with Righter's claim, and adds that, “People ordinarily spoke Prakrit, a descendant of Sanskrit. The [Ashokan] inscriptions were in Prakrit, not Sanskrit, presumably so that htey could be more widely understood by the people (204).”