The universe didn't start in a big bang. The cosmic background radiation doesn't have to come from that. That's magical thinking, and always was.
The data points to the big bang is the most likely beginning of time by a long shot. But not 100%.
Hubbles law, background radiation, nucleosynthesis, and galactic formation all strongly support a big bang
Hubbles law, background radiation, nucleosynthesis, and galactic formation all strongly support a big bang