This took all day, but this is a general timeline of the events that took place in Blaire's life. Please note that I've canon diverged slightly with some of it, but have otherwise done my best to keep things as canon compliant as possible. Also please note that this timeline touches on things such as murder, police brutality, and other such unpleasant topics!
January 10th, 1995: Blaire Sullivan is born.
June 2000: A home robbery turned double murder happens on a hot afternoon. Blaire, who was five at this time, hid in her closet and unfortunately heard the entire thing from start to finish and had to be gently coaxed out of her closet by law enforcement. This is the only time that she trusts law enforcement, sadly, as her parents' killers were never found, even with an extensive investigation being launched. As her only living relatives were, at the time, John Kramer and Jill Tuck, she was sent to live with her uncle John, even despite his own cancer diagnosis.
June 2000 - October 2004: Blaire's involvement in John's games as Jigsaw is nonexistent as John does his best to raise her like the child he never got a chance to have.
Sometime in 2004: The events of Saw X take place. As John is desperate to find any kind of treatment for his progressing cancer, a recommendation from a fellow member of his support group gives him hope. It's an experimental treatment, but it's better than nothing. The trial is helmed by Dr. Cecilia Pederson instead of her father, but is still promising nonetheless. John travels to Mexico City with Blaire, where she meets with the doctor and her team: Mateo, the anesthesiologist, Valentina, the nurse and Dr. Cortez along with patients Gabriela, Parker and Carlos, the caretaker's young son. Although the team's promising their best, Blaire can't help but feel like something's amiss, which she tries to tell her uncle about. When his surgery is underway, she's kept busy with Gabriela and Carlos instead of being allowed to be by her uncle's side or to help set his room up.
When John finds out that he's been a victim of a scam after coming across the place where his surgery supposedly took place, it prompts him to start up a game right in Mexico City to teach Cecilia and her team a lesson and bring Amanda in. As Mateo, Valentina, Cecilia and Diego were captured, John kept Blaire busy by taking care of her as well as instructing Amanda to keep her safe. The games proceed apace until Parker appears and turns the tables on John, Amanda and Blaire by forcing John and Amanda to chain themselves up like they did with Cecilia, Mateo, Valentina and Gabriela. However, since Blaire wasn't chained up, she was able to save Gabriela before Cecilia remorselessly killed her after she rightfully won her game. Angered by this, Cecilia roughly yanked Blaire up by her hair right in front of John and Amanda, but undeterred by this, Blaire demanded Cecilia and Parker to let Gabriela go and get the medical attention she desperately needed. Reluctantly, they agreed and placed Blaire in the same chains that John and Amanda were.
Due to Blaire's act of mercy, Cecilia thought it was fitting to place her in the same trap that she was supposed to undergo: the bloodboarding trap. As both John and herself were in chains, the trap set off and Blaire, wanting to spare her uncle any further suffering, tried to take as much of the blood that was pouring on them as possible, even when John insisted that he was fine and could take it all. This earned a great deal of ridicule from Cecilia and Parker, who thought that they got one up on the infamous Jigsaw, but as their own hubris got the better of them to where they were trapped after trying to get away, John was able to get free along with Blaire and Amanda in tow. He apologized for the carnage that Blaire had to witness as they left the villa that they were in.
October 2005: Blaire's involvement in John's games continue as she helps tend to her uncle, who at this point, is on oxygen and pain medication. She, at just ten years old, witnesses the brutal beating her uncle is given at Eric Matthews' hand, which only furthers her distrust in law enforcement.
April 28th, 2006: John's final game commences where it seems like he's testing Dr. Lynn Denlon on her ability to keep someone alive, but in all actuality, he's giving Amanda one last chance on HER ability to keep someone alive. During this time, Blaire's mentally preparing herself for the death of her uncle and is periodically checking in on him to see if there's anything that she can do for him. It's here that she's told, out of earshot of Amanda or Lynn, that he never intended on involving her in his twisted line of work and understands if she resents him for how monstrous he really is.
Still believing there's a shred of good still left in him, Blaire tells him that she doesn't resent him at all and knows that he tried his best to give her some semblance of a normal life when he could. After this, John gifts her a necklace and instructs her to keep it on her at all times.
During this, Blaire takes note of how Hoffman switches up a note in an envelope that was meant for Amanda. With her curiosity getting the better of her, Blaire went to ask him what it was that he was up to. Since Hoffman knew she was only a child at that age, he told her to just run along and go play. She didn't fully buy his explanation, however, but did as she was told at the time.
When her uncle was murdered by Jeff Denlon in an act of vengeance, Blaire was temporarily in the care of Mark Hoffman since her aunt, Jill Tuck, was out of John's life at this time, and was subsequently being interrogated by police at this time for her supposed involvement in the Jigsaw murders. Logically, it wouldn't make sense to release a minor into her care, especially since Blaire could very well have evidence of her own to help police with their case.
May 2006: Jill gains custody of Blaire, asserting her right as her only living guardian, even despite them both being questioned by law enforcement during this time. Due to how the police and FBI have shown her their true colors in the past by both deciding that brutality was a better option than calmly interrogating her uncle in the form of Eric Matthews and by failing to find her parents' murderer(s), Blaire doesn't tell them anything, instead remaining silent as it is her Fifth Amendment right to do so.
June - July 2006: Jill exacts John's final request of her to punish Hoffman for deviating from his plans and using his games to further his own narcissism. Hoffman was expected to die as a result, but escaped the Reverse Bear Trap that was placed on his head. He decided to lay low for eight months after these events.
March 12th, 2007: Due to the increasing threat on both of their lives, Jill and Blaire both go into Witness Protection under Matt Gibson's watchful eye in the Metropolitan Police Department, much to Blaire's chagrin since she doesn't think that the police will be enough to protect them from someone as determined to kill them as Hoffman is. Jill tells her not to worry since things are gonna be okay, but Blaire doesn't believe her. Her suspicions are correct when Hoffman, using a body bag to get into the police department so as to get close to them both, murders all opposition in his way. Jill tells Blaire to run before she sticks a nail file into Hoffman's neck as Jill runs into the evidence room to hide. Blaire doesn't dare look back during this, using her smaller height to her advantage to slip past Hoffman to safety.
Having a feeling that nowhere inside the police station would be safe, Blaire instead runs outside while the doors are still unlocked. This turns out to work in her favor until she runs out of energy and stops at Saint Eustace Hospital, all but practically demanding to see Dr. Lawrence Gordon. Once she was situated, she told Dr. Gordon everything that went on and how likely it is that Hoffman is the one who killed Jill. This prompts him to act immediately with him promising that she'd be safe now.
On that night, Dr. Gordon, along with Ryan and Brad from the Public Execution Trap, all help take Hoffman down with anesthetic while Blaire is recovering in Dr. Gordon's office from the trauma of what went down this fateful night. It's this night where Hoffman is dragged to the very same bathroom that Dr. Gordon's game took place and is not given any method to escape, thus sentencing him to death.
2007 - onwards: Blaire takes a long time to not just gather whatever scraps she can from her life and build from there, but also to try to recover from everything that has happened to her at such a young age. From her parents' murders to witnessing her uncle get brutally beaten and die in such a short time frame along with losing her aunt as well, it left her rather traumatized as a result. Therapy did nothing to help her, but what did help was applying herself to countless hours of schoolwork to where she frequently achieved top marks on all of her tests at school, even though she was friendless. It was difficult for her to make any meaningful connections with people, however, due to how distrustful she was of others and how much she views herself as a bad luck charm because of how those closest to her ended up dying no matter what.
What also didn't help was that, no matter how hard she tried, because of the press lumping her in with her uncle, the stigma of her, too, being the Jigsaw killer never quite went away. Kids at school would frequently deface her desk with rude messages, even going as far as to cover it with a bucket of fake blood.
Still, none of these bullying attempts would be enough to spiral her into continuing her uncle's sick and twisted games.
She got to skip a couple of grades due to how hard she applied herself and graduated high school in 2011. The next year, in 2012, she'd enroll in MIT and work hard on pursuing both a Master of Engineering and Master of Science in Engineering degree, both of which took her two years each to complete, which would finish her schooling around 2016.
2016: The very same year that Blaire was able to earn both degrees is when she catches wind of the police suspecting her uncle supposedly having the ability to rise from the dead to continue his sick games. As his only living relative, she was immediately brought in for questioning to see if she had any involvement in this. Knowing her rights, Blaire refused to answer their questions and was released back into the custody of her guardian, Dr. Lawrence Gordon.
Though, this act raised both of their suspicions that something was amiss by someone trying to implicate a dead man in crimes he couldn't possibly have committed a decade later.
2016 to 2021: Blaire has since become a successful and famed engineer, using her talents for good and following in her uncle's footsteps in enriching others' lives with her own urban renewal projects.
2021: Although, the suspicion that there's a copycat Jigsaw on the loose is confirmed when word gets out about police officers dying in traps that are designed just like his were in 2021 — only this time, the copycat isn't as methodical as her uncle was and is only creating a mockery of his work. They say imitation is the sincerest form of flattery, but Blaire disagrees with that sentiment.
To her, this copycat must be dealt with at all costs, even if she must be the one to teach William Emmerson a lesson he soon won't forget. Oh, and don't worry, her lessons are particularly brutal to witness.
Her first game as Jigsaw takes place after she's successful in abducting Emmerson and puts him into a trap of her own design in order to teach him a lesson. Much like her uncle's traps, her own are designed to be escapable.
For Emmerson, his whole game was based on the concept of forgiveness. However, there was a twist to it all. Instead of his fate being up to him, it was instead up to what remained of the precinct that he personally had a hand in destroying. This required Blaire to abduct those that still remained: Drury, Deborah Kraus, Jeannie Lewis, and most notably, Zeke Banks. In her tape, she introduced herself as Jigsaw to the officers and told them that the man before them was responsible for the deaths of their fellow officers over the past few days and that she'd understand if they cannot find it within themselves to forgive him for what he has done since their colleagues are no longer with them. She also made it important to note that, because of his trickery, that it led to Zeke's father being unfairly gunned down by SWAT by a gun that was planted on him.
Needless to say, forgiveness was in short supply for what remained of the South Metropolitan Police Department, which sentenced Emmerson to his death, even though he tried to appeal to their good sides.
As for them? They were all free to leave. Thinking that they were all going to die, they asked the recording why, but didn't get an answer.
Present day: Blaire is still keeping tabs on things to see if any further copycats spring up and need to be taught a lesson on imitation while she works on enriching the lives of others.