Activate Blasting Station by tapping it and sacrificing Lesser Masticore.
When Lesser Masticore dies, its persist ability triggers, returning it from your graveyard to the battlefield with a -1/-1 counter on it.
Thran Vigil and Blasting Station trigger.
Resolve the Thran Vigil trigger, putting a +1/+1 counter on Lesser Masticore.
Resolve the Blasting Station trigger, untapping it.
Resolve the Blasting Station ability from step 1.
Repeat.
This loop turns Lesser Masticore into a self-sustaining projectile by exploiting its persist ability, which brings it back with a -1/-1 counter whenever it dies. Blasting Station provides both the sacrifice outlet to send the Masticore to the graveyard and the damage-dealing engine to win the game, instantly untapping itself each time a creature enters the battlefield. Meanwhile, Thran Vigil watches over your graveyard and neatly neutralizes the persist drawback by placing a +1/+1 counter on the Masticore as it leaves, annihilating the -1/-1 counter so the whole cycle can repeat indefinitely.