How can we be 13.2 billion light years from another galaxy? How did we get 13.2 billion light years from the faraway galaxies being discovered with Hubble?

If we all started near each other at the Big Bang, and we all travelled slower than the speed of light, and the universe is about 13.9 billion years old, how could we possibly be 13.2 billion light years away from recently discovered galaxies?

I know "inflation" was supposedly superluminal, but I bet no one thinks that matter dispersed several billion light years apart during that operation.
The distance you are referring to is the "light travel distance". It is the length of time that light has been travelling from the distant galaxy to us.

When the light was emitted, our Galaxy was much closer to that distant galaxy. What has happened in the meantime is that the space between the galaxies has expanded.

Furthermore we can ask where is that galaxy right now (where now is a time measure since the big bang) and it turns out that the galaxy would be much further away than 13.2 billion light years - more like 40 billion light years if you were to somehow measure that distance with a very long ruler.