Here's a neat diagram that will help you see the events happening in a chronology.
(Source : Predestination Timeline ExplainedPredestination Timeline Explained)
The link has a lot more detailed explanation.
Follow it from the Pink, to the Blue to the Green for chronology. It would be:
- Jane left at orphanage
- Jane meets and falls in love with an unknown man (John)
- Unknown man (John) leaves Jane on the park bench
- Jane is pregnant, delivers baby, baby is stolen by unknown (Barkeep)
- Jane becomes a man - John, the unmarried mother (Pink to Blue)
- John meets Barkeep
- John travels back in time with Barkeep
- John runs in to Jane to reveal that John is the unknown man
- John leaves Jane on the park bench
- John and Barkeep travel to the future, John is enrolled as a temporal agent.
- John prepares to become a temporal agent.
- John travels to diffuse one of Fizzle Bombers bombs, gets his face burnt
- John returns to the bureau in the future and gets a face graft to become Barkeep (blue to green)
- Barkeep goes back in time to meet John at the bar
- Barkeep takes John further back in time to get John to meet Jane
- Barkeep leaps illegally to catch the Fizzle Bomber, gets John to burn his face as a result
- Barkeep goes back in time to the hospital and steals Jane's baby.
- Barkeep takes it further back to leave the baby at the orphanage
- Barkeep travels forward to collect John who leaves Jane at the park bench
- Barkeep and John travel to the future, Barkeep enrolls John in the bureau.
- Barkeep retires, goes back in time and tries to decommission the time machine
- Time machine fails to decommission, Barkeep finds clues to the location of the Fizzle Bomber
- Barkeep goes to the laundromat to find the Fizzle Bomber, who is merely an older version of himself.
- Barkeep kills his older self - the Fizzle Bomber
- Barkeep doesn't report the un-decommissioned time machine and eventually becomes the Fizzle Bomber (Not shown in the movie)