CPG happened a good 2-3 decades before the 'Broken Mask'.

From what we can gather in game, the most useful data being from within the Institute itself the CPG was a project initiated by the Institute to form a Government that after three years of development nothing was really achieved as the wastelanders of the time couldn't come to terms with anything. This eventually lead to the massacre of the CPG. However while the Institute are blamed for this incident there is no proof they were at fault and could of very likely been the towns and settlements figure heads killing each other with the Institute taking the blame due to sending disposable androids rather then humans.

It actually makes sense if we are to assume the Institute were not at fault for the massacre. After the CPG massacre wastelanders start destroying synths in 'retaliation'. Despite the Institute's good intentions at the time the Wasteland rejected them with fear and paranoia. Logically this would make a perfect point in time where those within the Institute decided, "fuck the wastelanders, why bother helping bunch of ungrateful psychopaths". Something along those lines.

After that they stopped trying to interact with the surface and grew more ruthless. No longer caring about the people above they started working on their Gen 3 Synth to replace the filth above. Thus is lead to Kellogg being hired, Vault 111 raid in 2227. By 2229 they had a working Gen 3 prototype that may or may not have malfunctioned. The rest is history.

Now naturally this is all a theory. To me at least it would explain the Institute who were likely moving towards the dark side of humanity experiments with FEV and sentient robots, pushed over the edge by no longer caring about the rest of humanity who rejected their attempts at cooperation. This seeded a deep hatred for the surface that leads to their moronic beliefs of 2287.