u/ConfidenceKBM

The Syndicate existed in the show, as did Phelps, so even though it wasn't part of the first film we can certainly say, retroactively, it existed at that time. Kittridge tells Ethan that there's been "serious blowback" in IMF operations, so Jim has been sabotaging missions before the movie starts. Exposing literally all NOC agents is definitely something the Syndicate would want to do.

 

Iirc the syndicate in the fifth movie only consists of presumed dead or disavowed agents, and Phelps wasn't either of those, but still... Krieger was disavowed though, I'd say it's a near certainty that Krieger was in the Syndicate, and he was connected to Claire and Jim.

 

Maybe we can at least say that Max was a middle-man for the Syndicate? She was trying to transfer the NOC list on the train at the end, I don't think it's ever said who she was sending it to. Overall the first movie feels like a Syndicate story without the name.