It has been stated several times here and probably elsewhere that the first population III stars were unable to undergo H-to-He fusion via the CNO cycle as there was virtually no carbon-12 at the point of the first stars forming, and they were stuck with the pp chain.

What I have a question about though is that it has been shown that there were $~4 \cdot 10^{-16}$ carbon-12 nuclei formed for every proton in primordial nucleosynthesis. This means there was around 10^65 carbon-12 nuclei already in existence which seems to indicate there would definitely be a non-zero probability of the CNO cycle being able to function in the earliest stars. It may have not been quite as dominant as it is today in high mass stars but it seems like it would have had an impact right from the beginning.

So how come it is still stated that the CNO cycle couldn't have happened in the earliest stars when it seems that the material needed for it was already present (granted not nearly in as high amount as it is today)?