Say it is the universe rather than just the galaxy. The universe has no edge, but rather than having no center, each entity at whatever scale, quark to atom, to molecule, to biosphere, to noosphere is it's own center, all sharing the same coordinates of space and time from center to as far as it goes. UCANSEE2, both UCANSEE2-- bio-entity with trillions of Kreb cycles per second, and UCANSEE2--cybercreature, is the center of all. There are other centers, each particle, whether elementary particle or higher construct is a center. The center is a plurality. It's not 'no center', it's all centers.
Statement should have been: First, if the UNIVERSE has no edge, it has no center.
Second, to answer the questions posed in your response, if all entities have a common center, then the question of distance between them, or measurement of their speed relative to us, or anything else, is pointless.