From the very first episode of Doom Patrol, viewers have wondered if Crazy Jane had the power to travel in time. With Crazy Jane possessing 64 personalities, each, in turn, possessing their own special superpower, the possibility is certainly there. Yet there is other evidence of Jane's being a chrononaut in the episodes aired so far, which would also explain some of the apparent inconsistencies of the show's timeline.
The possibility of Crazy Jane being a time-traveler was first suggested in the Doom Patrol pilot. The first episode largely centered upon Cliff Steele, as he adjusted to his new life as Robotman, with a montage showing that Cliff first came to Caulder Manor in 1995 and lived there until the present day. Cliff then meets Crazy Jane, whom Rita Farr complains "comes and goes as she pleases, like she owns the place," despite Jane apparently not having visited the mansion in at least 24 years. When Crazy Jane and Cliff talk later in the episode, she claims that she first met Dr. Niles Caulder sometime in the 1970s, despite not looking a day over 30.
This raised several question about Crazy Jane's past and her age. While every other member of the Doom Patrol cast has a reason for being virtually immortal, there is no apparent reason why Jane should be able to resist the passage of time. The idea that one of her personas had the ability to travel in time would explain this, allowing Crazy Jane to go back in time to meet Dr. Caulder at the proper time and pop into his home whenever she wanted. Yet there was also the possibility that one of Jane's personas offered her some degree of immortality or eternal youth, like the ever-young and optimistic Baby Doll.
The idea of Crazy Jane as a time-traveler did gain some credibility with "Paw Patrol" - episode 5 of Doom Patrol season 1. The episode further detailed Crazy Jane's origins, showing that an adult Jane gained her powers in 1976 and first visited Caulder Manor in the winter of 1978. Between those two moments, however, we see one of Jane's personas in a mosh-pit at a punk club in 1977, wearing a T-shirt which makes reference to Time Travel. Given that Jane's personas change hair, clothing and make-up as they take control (For instance, Babydoll's hair always changes to pigtails) this could be a sign that one of Jane's personas has the power to time travel.
The possibility of Crazy Jane being able to time travel was also suggested in the Doom Patrol comics. One of Jane's personas, Flit (who has also appeared on the show) was shown to have the power to teleport through space and into other dimensions. While she was never specifically shown as being able to travel through time as well as space, the possibility is there depending on the nature of physics in the DC Universe and whether or not Flit's ability can work in the same fashion on the show.
Sadly, there is little in the way of solid proof that Crazy Jane is a time-traveler. On the other hand, there is nothing that outright eliminates the possibility either and there is much to suggest it is not only possible but probable that Crazy Jane can travel in time as well as space. With any luck a future episode of Doom Patrol will address this, making it just a matter of time before we have an answer.