I’ve been investigating the topological Casimir effect from compactified dimensions as a mechanism to explain dark energy, and this raised a question I was hoping someone could shed some light on. I have always thought of the Big Bang as a SIMULTANEOUS decompactification of three compact dimensions, using the terminology of string theory.  Is there any evidence that decompactification progressed stepwise instead? Say from a 0+1 to a 1+1 (spatial + time-like) or from a 0+1 to a 2+1 expanded dimensional space before finally acheiving a 3+1 expanded dimensional space? If so did this lead to prior false-vacuum states that might be linked to Inflation?

More specifically, is there any hint of a stepwise decompactification observable in the Cosmic microwave background, or is there any evidence of asymmetry in the Hubble expansion field? If not, why does the big-bang require simultaneous decompactification of three spatial dimensions? What is special about 3 non-compact spatial dimensions?

Related question: If there was a stepwise Big Bang dimensional decompactification, could this have lead to large scale fluctuations in the background distribution of mass/energy, leading to early structure formation?