As seen in my run you can start game with first door already opened. It seems that game is not clearing triggers between attempts.

Start New Game, go to the water tank. Interact and immidiately Esc -> Main Menu.

Now when you will start New Game, trigger will still be active and door will open.

This means that before each attempt there is short setup needed. However it is short and easy enough that I belive that those few second gained are worth it.