I recently watched the 2022 director’s cut of Star Trek: The Motion Picture to compare it to the original 1979 release, which was based on TOS. It reminded me of an ongoing rumor and speculation in Star Trek fandom that V'Ger and the Borg may have a shared ancestry or common origin. The Motion Picture is set in the 23rd Century, and the crew of the USS Enterprise is on a mission to investigate a mysterious energy cloud.
As the story progresses, we learn an alien craft is enveloped inside the energy cloud. The cloud is expansive the size of 2 AUs (Astronomical Units). Regarding the massiveness of this energy cloud, 1AU is the distance between the Earth and the Sun, which is a staggering 92.9K miles.
When considering if V’Ger and the Borg had some common ancestry or if one created the other, we must first look at where they were in space and time relative to their possible origins. The Borg Queen in Star Trek: First Contact (1996) took place in the 24th century. She explained The Borg existed over a thousand years ago in the Delta Quadrant.
This means the Borg would likely have been created and assimilated other species primarily in the Delta Quadrant during the 15th Century and earlier. V’Ger was launched in the Alpha Quadrant centuries later in the 22nd Century on an interstellar journey, for 300 years, on a mission to “learn all that is learnable and return to the creator” – humans on Earth!
Given it's our understanding that space and time are not necessarily linear, it’s unlikely that V’Ger would have managed to navigate space and time, accidentally or intentionally, to get to the Delta Quadrant. It's certainly unlikely the V'Ger would have used resources to travel to the Delta Quadrant when its prime directive was to report its knowledge-seeking findings to Earth in the Alpha Quadrant.
Of course, it’s possible The Borg could have traveled to the Alpha Quadrant to encounter V’Ger or V’Ger could have been captured in a black hole, a trans warp conduit, or some other potential time-bending anomaly to travel back in time to encounter The Borg a thousand years in the past. Contemplating Star Trek lore, either of these scenarios could be possible; however, there is no known Star Trek canon to affirm these likely.