Practice, practice, practice.
When you leave, don't say anything except "stay" (or whatever command you use). Don't turn around and look back. Don't make it a big deal, just walk away and get OUT OF SIGHT. This part is important. As long as he can see you, he's going to fuss and cry and try to get your attention. In training, it's ok to have the person holding him give him treats, or take him for a little "walk" in the opposite direction, to get his mind off you.
I am a dog groomer by trade, so people hand their dog to me and leave several times a day. Most dogs who fuss about their owner leaving are actually much better once the owner walks out the door and is out of sight. Then the person holding the leash (me) is the new "mommy". Usually the dog will go straight into a crate, but sometimes I'll take them out back for a short potty walk, and sometimes they go directly into the bathtub. Most of them calm down in a reasonable amount of time, but puppies can be rather fussy for the first couple times they come in. It just takes time, patience, and maturity.
In my grooming shop, key to keeping the dog calm is that the owner is GONE. Really, truly, gone out of sight, scent and hearing. Most dogs stay with me for at least 3 hours, and almost all of them stop freaking out by then. But you can start slow and gradual, like just handing the leash to someone, walking ten feet away, and turning your back to the dog. Then come back as soon as he is calm, and praise him calmly. The whole process has to be matter-of-fact, no big hullaballo about it, no big party when you come back. If anything, the person holding the dog can give praise and treats when the dog is calm. It takes time, patience, and maturity. Did I mention that?
You might want to consider putting off the CGC until he matured a bit more, there's no shame in that!