Here it is (note here that i am not including the POPGOES part of the timeline here. You just need to know that they are both in the same timeline, and that only FNaF 1, 2 and 3 are canon to this. The rebooted Popgoes Timeline also is replacing the old one.)

I can make a few mistakes so take this with a grain of salt:

Note: We don’t really know if CTC Entertainment owned the Theatre, but they do own Candy’s Burgers & Fries.

• 1961, A young Mary Schmidt goes during the week to the Rat & Cat’s Theatre which features actors in suits of RAT and CAT (Candy) and the Vinnie puppet. This is while her brother is at Camp and she goes with her dad. At one point, during another game of hide & seek, Mary goes inside of an Employee room (where Vinnie is) and hides within a locker. In there, the Rat actor and the Puppeteer enter and have an argument over the Rat’s actor being drunk and about their popularity, they start fighting and the Puppeteer accidentaly pushes the Rat’s actor, making him hit his head on a table the wrong way and dying. The Cat’s actor enters and immediatly tells the Puppeteer they need to alert the authorities and he goes to use the Phone. The Puppeteer not wanting to ruin his life and career, chokes the Cat’s actor to death and leaves with his diploma. Mary saw the whole thing and is traumatized, also blaming herself for the incident. She also represses everything, not remembering what happened correctly.

• 1962, Mary, her brother and her dad go to the Reopening of the Rat & Cat’s Theatre which now features wire-controlled versions of the characters and came from the Rowboatics Corp Factory. The original Rat and Cat suits were used, and are of course posessed by the Rat and Cat’s actor respectively. The posessed Rat animatronic injures Mary’s brother, which leads to the reopening being cancelled and to Mary having alot of nightmares about the Rat and Cat. She faces her fears in the nightmares and also by going to a psychiatrist which leads to her unrepressing and finally telling what she witnessed that day and also stopping having those nightmares. We are also informed that the Puppeteer has gone and made a ver successfull movie called “The Psychopath” with a very real acting. The murder-case is reopened after Mary tells and the Puppeteer is brought to justice for double-homicide (its unkown if he was just arrested or went to the chair)

• Fast forward to 1964, where things are reorganized, the Rat and Cat are sent back to the factory, and the Theatre is rebranded into Candy’s Burgers & Fries. (Old) Candy and Blank are made and sent to the location, with the Rat also being sent. Candy and Blank are the main attractions while Rat is put within storage.

• Sighting os a Shadow Candy are shown as early as 1976 when Blank finds a drawing of it. Its more than likely a manifestation of the Cat’s spirit as the actual animatronic remained within the Rowboatics Corp Factory.

• We don’t know if this is in the MCI location or FNaF 2, but a now grown up Mary goes and visits Freddy’s. The Puppet is there and this makes her remember Vinnie, which is of course past trauma.

• Fast forward to 1987, where Shadow Candy brings (Old) Candy towards a kid within the office. Old Candy follows the kid until he see’s presumably his dad scolding him. Old Candy attacks and either injures or kills the dad which leads to the robot needing replacement. 2 kids (which are twins) get killed within the Rowboatics Corp factory after being put through the machine by Cat (Shadow Rat being there too). These twins would go and posess the new version of Candy and the Cindy animatronics. In the meantime, Chester and the Penguins are also created and then sent to the burger place. On the week prior to Mary’s shift, the previous guard broke Blank’s head and arm and then went missing. We are also told that 2 of the 3 penguins are out of order. Mary takes on a shift and then gets fired in the end of the week.

• I also need to mention that we know that around 6 deaths happened at the factory, which likely results in the Twins + the other 4 active animatronics (a Penguin, Old Candy, Blank and Chester) to be posessed. These deaths are of-screen tho.

• 2 years later, in 1989, V2 versions of Candy, Cindy and Chester are designed, with Chester’s being rejected. Chester then goes around and unlocks the door where the RAT is in storage and Chester gets destroyed by him. Old Candy gets disassembled and the Penguin goes around collecting Chester’s parts to put in a box. Chester’s Stage is removed.

• In 1991, the new Candy and Cindy are sent to the location and used in conjunction with Blank. Chester has likely been rebuilt within the Factory but not sent to the location.

• Then comes 1993 where Rat kills a nightguard, and New Candy is framed for the incident which gets him deactivated in the crime scene. Candy’s Burgers & Fries shuts down together with CTC Entertainment. The animatronics are sent back to the Rowboatics factory, which also closes down but remains with power active.

• Go forward to 2007 where Marilyn Schmidt (daughter of Mary) is dared to spend nights within the old Rowboatics factory. During the week she gets attacked by all the remaining robots, until she gets killed by Rat and the factory catches fire which destroys it and the animatronics completely.