As far as specifics, I don’t think there is one specific thread that makes it a Cloverfield movie, I guess.
It was written before 10 Cloverfield Lane and the expanded Cloverfield universe even existed as a thing.
Paramount is building out their Cloverfield universe and will do so this year by turning God Particle into Cloverfield 3.
While this could result in massive changes to the film’s original design, the screenwriter behind God Particle has revealed how this evolution of the project came to be.