The Vedas actually are fairly aniconic, and so the depiction of what we call today the Hindu gods was relatively late, not until the early centuries CE with he development of so-called Puranic or Shramanic Hinduism. This in turn was probably a result of influence from Buddhism, which in turn may have been taking cues from Gandharan art, which was influenced by currents in Western Eurasia. But that particular thread is a bit difficult to trace back so don't take this as the only potential interpretation. It also isn't completely relevant except insofar as it reminds us that these particular depictions are not as old as the Vedas.

Looping back, the figural representation of the Hindu gods shouldn't be taken as literal depictions, to the extent that a literal depiction even makes much sense. Rather, by depicting the multiple arms or multiple heads the artist is able to combine the different aspects of a particular deity that they want to depict. For a largely illiterate population, visual communication of ideas such as this is extremely important in the popular dissemination and depiction of religion. A very common comparison is to a stained glass window, which communicate particular Biblical or religious stories without requiring a literate audience.