In order for us to receive light that originated 13.0 billion years ago. We have to be 13.0 billion light years from where that object was 13.0 billion years ago. True statement?
So if the galaxy speed is 0 then the entire distance is due to either inflation or the initial distance between the objects at the big bang.
And if the universe was small at the big bang. Say 1 billion light years wide. Then inflation must acccount for 12 billion light years of distance in 13.0 billion light years for us to be in position to receive the light. That means inflation is a high percent of the speed of light
Substitute “expansion” for “inflation” and you’re basically correct. “Inflation” is a term reserved for a particular theory of the early universe. But your last statement “inflation is a high percent of the speed of light” needs some correction. The speed of expansion is proportional with distance. It’s called the Hubble Constant, or Hubble Parameter. It’s estimated to be about 70 kps for every million parsecs, or 3.26 million light years. So at a distance of about 14 billion light years, expansion exceeds to the speed of light. We can’t see beyond that, obviously, which defines the visible horizon.