So we all know you can lose without having a turn ...

... have Father Dagon as the Herald, have the first pre-game Mythos card open a gate on Devil Reef, have the second (thankis to Father Dagon's text) pre-game Mythos card cause a Monster Surge, with 6+ monsters now on Devil Reef they all move into the rift and fill the Deep One Rising Track instantly, if Azathoth is the Ancient One then game over ...

But is this scenario for winning the game without having a turn legal?

In a one player game, use Akachi Onyele as your Investigator. She starts the game with a gate trophy and if the pre-game Mythos card doesn't open a gate - say The Next Act Begins - then as the first turn starts you have 0 open gates and a number of gate trophies equal to the number of players ...

I believe that the endgame condition is only met if the "last gate on the board is closed." Therefore, most situations involving Akachi will not work like that.

HOWEVER!

If you're playing a 1-to-3-player game (depending on how many expansion boards you're using) that includes Akachi, and this is your first Mythos card:

...then you win on Turn 0

De Vermiis Mysteriis from Dunwich Horror lets you roll a check on your movement to close an open gate. I actually played a single player game and got that item in my starting items. I won the roll and won the game. Technically it was on movement on turn 1, not so I did have some of a turn, but still, pretty nice.