What is the earliest moment in the game where I can kill Phineas Welles?
Phineas is the one person you cannot directly kill in the game. That's exactly why the game designers have put him in the lab, Phineas is the catalyst of the main story (whichever way you go) and the main story would stall without him.
It is possible to kill Welles.
You can kill him as the last enemy of the game if you side with the Board. Take the quests to turn him in, starting with the board representative on the Groundbreaker. The plot will proceed similar to the normal game, but Welles will be the last fight.