In the episode "The Red Forest," we deal extensively with a timeline where Cassie dies in 2015. In fact, this timeline's existence is crucial in providing Cole with important information about Operation Troy.
Now, in the season 4 episode "One Minute More" we've learned that
Hannah Jones is Cole's mother.
However, in the timeline we see in the "The Red Forest"
Jones was still committed to working on time travel at Raritan in 2043. We know her motivation for this was to save Hannah, so Hannah must've died in this timeline.
Ramse still knew Cole, but he had already died in this timeline.
So with both Cassie and Cole dead, and Jones knowing neither of them, it's clear that the events of the season 2 episode "Lullaby" could never transpire in this timeline, so...
How did Cole still exist in that particular timeline?