He is eternally begotten.
The act is God knowing Himself. His knowledge of Himself is the Word, God the Son.
However, because God’s self knowledge is a person, God the Son, the act is not so much an act as an intrinsic quality of the divine nature.
To put it more simply, to state that being begotten was an action would mean there was some point at which God had not yet acted and, thus, some point at which the Son was not.