Me: "such galaxies would have had to exist 100 billion years ago"
You: Inflation allows for recession speeds greater than lightspeed.
Yes, but the inflationary period ended early, before the formation of galaxies began. I was asked if we could see a galaxy 100 billion light years away from us. It's light wouldn't have had time to get here.
Add to that, the universe appears to be expanding even after the inflation phase. Someone above pointed out that the distant objects are receeding at faster than light speed and so can't be seen. This would put the observable limit of the universe at a particular distance from the observer