I agree, I don't see the C-clip but it's so small it's hard to see, it could also be stuck with another part.
Looks like everything is there, I would recommend getting a spare front pivot takedown detent pin, they're very easy to launch sometimes even if you use a clear plastic bag on top of it.
For extra reliability on carbine gas systems, I would also recommend the spring only of the BCM extractor spring upgrade kit, try out your standard carbine buffer first most usually the H heavy carbine buffer would work better, and use Magpul gen 3 mag followers and/ or Magpul PMAGs.
I built a lower for my dad which was my third lower build and it went very well, I used the Vise Grip pliers method in installing most of the roll pins, and staked the buffer tube castle ring, enjoy your build.
Ref:
BCM Extractor Upgrade Kit - link
AR15.com Parts Diagrams - link