CNO cycle requires the presence of carbon, nitrogen and oxygen to undergo hydrogen fusion. Does this mean that for first generation stars, no matter how big they are, can't undergo hydrogen fusion by CNO cycle because there is no carbon, nitrogen and oxygen present?
I can't seem to find any website which mentions this. All they say is if a star is large enough, it will undergo hydrogen fusion via CNO cycle, they don't specifically mention it having to be a second generation star.
The CNO cycle does take place in the earliest massive stars, but only once a significant amount of helium has been burned into carbon by the triple alpha reaction.
Massive population III stars ($>20 M_{\odot}$) cannot be supported on the "main sequence" by pp hydrogen burning alone. What happens is that they collapse until their cores become hot enough to trigger the triple alpha reaction. This produces carbon and once this has reached an abundance, by number, of about $10^{-10}$ of hydrogen (about 6 orders of magnitude greater than the big-bang C abundance), then the more rapid CNO cycle becomes energetically important (e.g.Ekstrom et al. 2008; Yoon et al. 2012).
In less massive stars there just isn't enough carbon for the CNO cycle to release a significant amount of energy (compared with the pp chain), but they can be supported (as main sequence stars) by the pp chain with interior temperatures too low to produce carbon (e.g. Siess et al. 2002). The CNO cycle can take place in later stages of their evolution.
It does require carbon to have CNO cycle fusion (it doesn't require nitrogen or oxygen, as they come from the carbon). So you are right, the very first stars could not do CNO-cycle fusion. However, it doesn't take much carbon to make it work, because the fusion is so extremely temperature sensitive that a paucity of carbon is easily made up for by a slight increase in temperature. But you do have to have a little bit of carbon from some prior stars, the Big Bang doesn't make essentially any.
