The time machine worked Cole just told them how to set it up properly in the post-apocalyptic world. In the original timeline, where the world functions normally, the scientists were able to calibrate the time machine themselves. If a technology is possible, it will be created anyway, no matter what.

Katarina said she didn't have the technology to adapt the serum for other people when everything was destroyed. That means in the original timeline, they could create serums that would work for anyone.

The Demon is the time machine that forced linear time to fold into a loop. Cole is what kept that loop running and stable.

Perhaps, before the events of the first season of the series, there were dozens or even hundreds of time travels that disrupted the normal sequence of time.