The usual handwaving for entropy v. information/complexity is to observe that our universe goes from simple low entropy state (Big Bang) to a simple maximum entropy state (Heat Death).

Both have low information. The complexity rises and falls, peaking somewhere in the middle, as energy from the gravitational field is turned into structure.

https://en.wikipedia.org/wiki/Weyl_curvature_hypothesis

Penrose likes zero initial Weyl curvature because it provides low entropy, but also conformal flatness, thus enabling his CCC theories.

Another consequence is that the Big Bang is not a reversed black hole (white hole). Black holes have high Weyl curvature. The Big Bang is the lowest entropy configuration, but a Black Hole is the maximum entropy configuration (just mass, spin and charges).