The references in the film are contradictory. At one point, Kirk says V'Ger came from the other side of the galaxy -- which is one piece of "evidence" that some people use to support the absurd notion that V'Ger was created by, or created, the Borg. But Kirk's information is thirdhand at best. I'd take the evidence from Spock's spacewalk as more authoritative.
In my novel Ex Machina
, I asserted that Voyager 6
had been thrown not only across huge distances of space, but thousands of years back in time, allowing time for the intergalactic journey over which V'Ger evolved and grew until it had reached the limits of knowledge on this plane of existence. I don't think it could've achieved that level in just three centuries of crossing a single galaxy. How could it have run out of things to learn about the universe if it had only seen one galaxy? (The more recent novel Cold Equations: The Body Electric
by David Mack uses the same assumptions about V'Ger's origins, since Dave wanted to stay consistent with what I'd done.)