Many teaching models of the big bang ask you to imagine the galaxies on the surface of a ballon that is inflating.
However, what many of them fail to remind you of is that you need to imagine that the galaxies are all two-dimensional and that you live on the surface of the balloon and can only see things that are on the surface of the balloon, i.e., that light travels only on the surface of the rubber, and you are incapable of perceiving anything either “outside” or “inside” the balloon.
Because the entire surface of the balloon expands as it inflates, if you lived in one of the flat galaxies, the other galaxies would all appear to move away, with the speed of their recession increasing with the distance they are away from you.
The “center of the universe” in this model is of course somewhere in the middle of the balloon, which is beyond your perception in this model.
Because this model presupposes a spherical shape to the universe, some propose an alternate model in which the galaxies are distributed on an infinite rubber sheet being stretched in two direections, which of course, unless it were curved into a spherical shape, would have no center.
The idea, which, again, many fail to teach when presenting this model, is to exptrapolate the insight you get from thinking about it in two dimensions into the real world observations in three dimensions. Three-dimensional galaxies are moving away from us in every direction because the universe is expanding in three dimensions, much like the surface of the balloon or sheet is expanding in two.
Some propose a model for thinking about this in the form of the galaxies being the raisins in an infinite loaf of raisin bread which is rising, spreading the raisins out in all directions.
We perceive ourselves to be a the center, but those who may be observing in a different galaxy will percieve themselves to be in the center.
The upshot is that there is no observable center. The whole thing is expanding.