You’re driving and see a huge patch of the fog suddenly turn red, I would argue you’re seeing break lights not fog. But that gets into definitions not just physics.
Similarly, the CMB is energy from the Big Bang as last scattered ~380,000 years later. IMO, that’s the Big Bang, but reasonable people can obviously disagree.
Everything is energy from the big bang, including you and me. But the photons of the CMB don’t represent anything that already existed immediately after the big bang. Protons and neutrons and hydrogen and helium were created in between, and inflation (probably) happened in between. The universe at the time of last scattering was a whole different world than a split-second after the big bang.
The Big Bang generally refers not simply to the instant the universe was created but an early high energy state. The term had long been in use before it was discovered that there needed to be an initial singularity. https://en.wikipedia.org/wiki/History_of_the_Big_Bang_theory
Or as an astrophysicist said ~”You can refer to the Big Bang as the first instant or a fairly arbitrary period after that initial event. The universe cooling down enough for matter is just as reasonable an end as the universe cooling down for atoms.”
