Even at the time the CDC gave its guidance, the published evidence to support the general public wearing masks was quite weak. Here is an extract from a systematic review of the published research from shortly after the CDC gave its guidance.
> There is uncertainty about the effects of face masks. The low‐moderate certainty of the evidence means our confidence in the effect estimate is limited, and that the true effect may be different from the observed estimate of the effect. The pooled results of randomised trials did not show a clear reduction in respiratory viral infection with the use of medical/surgical masks during seasonal influenza.
https://www.cochranelibrary.com/cdsr/doi/10.1002/14651858.CD...
So the CDC was faced with a situation where there was minimal evidence for the efficacy of the general public wearing masks and a severe shortage of PPE among medical personnel. In that context, they held back recommending that the general public wear masks.
It wasn't really till May/June that evidence started mounting in support of the general use of masks amongst the public.
So there was no conspiracy, just hard working people trying to do their best in a difficult situation. The world is much more dull than people like to believe.