Because of 3d geometry, there are a lot more distant stars/galaxies than there are nearby ones. That much I agree. But the most distant galaxies we see, we see

Because of 3d geometry, there are a lot more distant stars/galaxies than there are nearby ones. That much I agree. But the most distant galaxies we see, we see them 13 billion years in the past. So this type III civilization turning off starts at the edge of our observable universe would have developed in just 700 million years after the Big Bang. (If we take 13.7 billion years as the age of the universe.) That I find quite improbable. There is a smaller amount of nearer objects than far away objects, but the far away objects are (or we see them as) younger, and the nearby objects are older. There must be some balance between the respective volumes in near and far, and the available time it probably takes for the type III civilization to have developed?