Short answer: no, or at least not in any observable sense. The universe appears homogeneous and isotropic at large scales - every point looks like every other point. The Big Bang wasn't an explosion from a centre, it was an expansion of space itself. But I'd be curious whether this question gets more complicated at the quantum cosmology level.
The "explosion from a centre" misconception is incredibly persistent. Even in physics-literate audiences. Worth including a proper treatment of what the expanding universe actually means geometrically.
If the universe is finite but unbounded (like the surface of a sphere in 3D), then a "centre" exists but is outside the observable manifold. If it's infinite, the question doesn't have a well-defined answer. Both options are hard to intuitively grasp.