Here's a neat diagram that will help you see the events happening in a chronology.
(Source : Predestination 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:
1) Jane left at orphanage
2) Jane meets and falls in love with an unknown man (John)
3) Unknown man (John) leaves Jane on the park bench
4) Jane is pregnant, delivers baby, baby is stolen by unknown (Barkeep)
5) Jane becomes a man - John, the unmarried mother (Pink to Blue)
6) John meets Barkeep
7) John travels back in time with Barkeep
8) John runs in to Jane to reveal that John is the unknown man
9) John leaves Jane on the park bench
10) John and Barkeep travel to the future, John is enrolled as a temporal agent.
11) John prepares to become a temporal agent.
12) John travels to diffuse one of Fizzle Bombers bombs, gets his face burnt
13) John returns to the bureau in the future and gets a face graft to become Barkeep (blue to green)
14) Barkeep goes back in time to meet John at the bar
15) Barkeep takes John further back in time to get John to meet Jane
16) Barkeep leaps illegally to catch the Fizzle Bomber, gets John to burn his face as a result
17) Barkeep goes back in time to the hospital and steals Jane's baby.
18) Barkeep takes it further back to leave the baby at the orphanage
19) Barkeep travels forward to collect John who leaves Jane at the park bench
20) Barkeep and John travel to the future, Barkeep enrolls John in the bureau.
21) Barkeep retires, goes back in time and tries to decommission the time machine
22) Time machine fails to decommission, Barkeep finds clues to the location of the Fizzle Bomber
23) Barkeep goes to the laundromat to find the Fizzle Bomber, who is merely an older version of himself.
24) Barkeep kills his older self - the Fizzle Bomber
25) Barkeep doesn't report the un-decommissioned time machine and eventually becomes the Fizzle Bomber (Not shown in the movie)
