What is the shape of the universe?

Curvature of the universe seems flat but that just means its curvature is uniform.
Visible universe radius seems 13.7 billion years which is equivalent to 46 billion light years when expansion of the universe also considered.
All directions we look, start of the big bang (singularity?) is the border of the universe (which is a border in time).
The simplest geometry for the universe would be the surface of a sphere, but instead of 2 dimensional space curved in third space dimension, it is 3 dimensional space curved in time dimension.
(This means curvature of the universe can actually be calculated!)
Even though universe is physically similar from any point inside of it, from an observer point of view from anywhere in the universe,
it is like the observer and the point of big bang are located at the opposite poles of a sphere.
(Light rays sent in any direction would converge on the (same) big bang point at the other pole of the sphere.)
(But if so why Cosmic Microwave Background is not the same in all directions? It maybe explained by CMB origin is some time later than the big bang origin. That means CMB is like a circle around the big bang (pole) point. So light rays originated from the observer pole would hit the CMB circle at different points.
(Also density of the universe along each light ray could be different. Meaning CMB could be actually same in all directions.))
Also if the shape of the universe is really as described above,
that means size of the visible universe and size of whole universe must be actually equal!