Just a fringe speculation without any physical basis: maybe the Big Bang emits a 4-dimensional spherical shell of matter at c?

With the direction in which we are traveling at c called “time”, and the other three which we're not moving through called “space”;

diverging rays having spatial velocity relative to each other equal to tan(alpha) i.e. flat projection;

and at any given point on the 4-sphere's 3D surface everything appear to be diverging in 3D because the emission is spherically symmetric;

and trajectories sufficiently paraxial to us fits the small angle approximation but those diverging widely has much more apparent perspective distortion,

with an error ratio of tan(alpha)/sin(alpha) = sec(alpha) = 1/Lorentz_Factor?