I understand basically that the universe is homogenous (looks the same from every point) and I was told in my astro class that it's supposed to have no center, but how that works boggles my mind. I can't get over the feeling that from some point in the universe a civilization could look in a certain direction and see a sign indicative of the direction towards the edge or the center, like younger galaxies or a lack of galaxies moving a certain direction.
EDIT: Thanks to Sir Cumference for highlighting some things that are unclear about my question. Sure, to a certain extent you might be able to think of the universe as being without a center, but if you think of a ball growing larger from nothing, and you pick a random point in the growing sphere, you can always say that the point is further from some points on the sphere than others, or in other words, that there is a direction towards a "center".
Any other details you can give that are related at all would be extremely welcome.