Be going to is used to predict future events that are very near (and can be seen) or seem sure to happen. Such predictions are based on present evidence:
I'm going to faint. Look at the clouds; it's going to rain.
My sister is going to have a baby.
The expressions be on the edge / point / verge of (doing) something refer to actions that happen in the near future and have a meaning similar to be about to:
She is on the point of bursting into tears.
Researchers are on the verge of a breakthrough.