So from wherever you look, the universe is expanding away from you (I.e., other things in it move away from you).
Therefore, you can see that the universe doesn't have a centre. From this and some other a bit more complicated things, one can see that the Big Bang never had a single point but rather expanded everywhere at once when it happend. Although often called expansion from one point that is wrong.
Also technically you would need to give a time dimension as we live in 4D space.
Yes indeed, you could see every point as the universe as its centre (or none of them).