Okay. Lets assume you are correct, and CMB's are responsible for the first star formation. Why then are other observed clouds of helium and hydrogen not collapsing, since CMB's are everywhere?
If my understanding is correct, the radiation that we observe as the CMB was not responsible for star formation. The CMB is the result of the universe "clearing" when the first complete atoms formed. Prior to this the universe was made up of atoms without electrons which prevented any radiation from travelling too far. Once the universe cooled enough electrons were able to stick with atomic nuclei and the radiation was allowed to travel for long distances resulting in the CMB.