Consider the surface of a sphere. The sphere has a center, but it's not on the surface, so in a sense the surface has no center.
If you find that unsatisfying, you could posit that the universe does have a center, just not as a location in space that anyone could visit even in theory.
It didn't start from a single point - or at least - regardless of where you are, the the universe appears to be expanding outward from your location.
I don't know enough to say whether it started from a single point or not. But if it did, then every point in the current universe is where that single point expanded to. So, yeah, I can regard the point I am at as being the point that the universe started expanding from.