Jesus was begotten in the incarnation (Luke 1:35).
And yes, when Jesus spoke John 3:16, He had not yet died and risen; and after He would die and rise from the dead, there would be other sons.
Thus it is written,
Heb 1:6, And again, when he bringeth in the firstbegotten into the world, he saith, And let all the angels of God worship him.
Now, this means that He was God when He was begotten (brought into the world).
Also, God gave His only begotten Son to die on the Cross.
So, He was begotten before He died; and thus before He resurrected.