So the doctrine means not eternal generation, but eternal non-generation. Got it. :
Sending forth the existing God the Son to be God incarnate is not eternal generation but temporal designation.
To repeat:
It is that eternal and necessary act of the first person in the Trinity, whereby He, within the divine Being, is the ground of a second personal subsistence like His own, and puts this second person in possession of the whole divine essence,
What is the status of this second person before He was
put in possession of the whole divine essence?
The doctrine is false.