Nah just hear me out for a second
Spoilers below
I don't think there is a Loop 0. When Jack opens his eyes for the first time the blue haired woman has already been through dozens of loops before him. So even though that's loop 0 for Jack, for the blue haired woman she already been through many loops before Jack and none in those loops did someone got eliminated in the first night which explains why she told Jack that no one gets voted out during the first night.
Basically the whole game isn't really a time loop, it's a spiral.
Also I think the robot girl is the reason Jack got voted out in the first night , she must has rigged the voting just like the blue haired woman claimed.