Theory says there is no center, but every point is a center. To see this, consider the analogy of a two-dimensional world with time as the third dimension, where the two spatial dimensions are the latitude and longitude on the surface of a sphere (or balloon). The center of the sphere corresponds to time zero and, as the sphere expands with time, distances between points on the sphere expand uniformly in all directions on the surface.
There is no center on the surface of a sphere. Once the sphere is very big the surface is essentially flat. To a two-dimensional object like an ant walking on the surface, the surface would appear infinite, although it is actually finite, as the ant would never reach the end (though it could eventually return to the beginning of its journey).
The Big Bang model postulates that about 13.82 billion years ago according to the recent Planck Mission dating of the universe the part of the universe we can observe now was then very tiny. Technically it began as a mathematical “singularity” like a point of infinite density and expanded outwards from a hot very dense state into becoming the cooler universe we can see today.