Sorry if this or similar has been posted already. But here goes.
FNAF2 is a prequel in which you play as the murderer. You murder the kids during your week there. In one of the death mini games you play as the puppet, "giving life" to the dead children by putting the character suits on them. IIRC the old models don't actually come out until part way through the week, which means after Jeremy kills the kids, and the puppet stuffs them inside the suits. This is also about the time the police are investigating the restaurant.
Now the toy models could have witnessed the murder and gotten a clear view of the murderers face. This is important. Your main defense against the animatronics is your Freddy mask. You hide your face. The toy models are trying to scan your face, while the old models possessed by the dead kids are looking for a night shift guard. In both instances you are protected by a disguise. Now Foxy doesn't give a damn about your mask, but you can exploit a bug in their programming by flashing your light at them and making them reset. And the Puppet, who is still an attraction for the kids, can't leave his box while the music is playing because of his programming as well. That leaves all the others that are all fooled by hiding your face.
Now in night 6 you are told by phone guy they are shutting down, and that your last shift will be during the day. He also says he would take over the night shift when they reopen. I think Jeremy got his frontal lobe chomped during the day shift on Sunday because one of the new animatronics managed to scan his face and recognized him as the killer. The Bite of '87.
By now we can assume Fazbear entertainment is trying to cover up anything they can to save their reputation. They're committed to making this thing work despite all the problems they've had. This means firing anyone who get's too close to the animatronics and by association the evidence. So, they fire the night 7 guard (who is neither Jeremy, or phone guy who is still employed in FNAF1) for tampering with them, which might only be a silly tie in with the custom night thing, but it could also be Fazbear not wanting anyone near the animatronics. The restaurant is then shut down.
Time skip, to FNAF1, you're taking over the night shift for phone guy at the newly reopened low budget Freddy Fazbear's. You're in the new location, with the old models just as the news clipping said it would be. We know the new models were scrapped because of an issue with their programming. We can assume the issue was, that it was working perfectly. They were in fact protecting the kids from a murderer. The old models would have been in the back room during this event and never witnessed their murderer being attacked. Thus they still hold their vendetta against the night shift guard. While they can't recognize a specific face, they do want the night shift guard dead.
During his first week there phone guy is killed by the animatronics. Before he dies he asks that you do him a favor and check the back room with all the extra suits. He knew he was going to die and asked Mike Schmidt to find his body. Mike Schmidt is also terminated for tampering, but he was actually trying to find phone guy's body.
My problem is, I have no proper explanation for the puppet being alive in the first place. I don't want to leave this to supernatural behavior since that's not entirely out of the question. Based on the theory that the animatronics are possessed, since that is also a supernatural occurence. My only other guess is that one of the kids possesses the puppet at the time of the murder, and then places the remaining 4 kids into the suits of Chica, Bonnie, Foxy, and Freddy. This would also tie in to the murderer wearing the Golden Freddy suit when he's killed, thus his appearance in FNAF1. Any appearance of Golden Freddy in FNAF2 could be hallucinations brought on by Jeremy's paranoia or guilt from the murders. Puppet ends up being scrapped with the rest, but the kid who possessed it still did set in motion the events following.
Also the disappearances of the children were said to have happened in June. But, it's heavily implied the murders occurred during the week that FNAF2 takes place in, yet the check is dated November? Is it just using system clock? Can anyone confirm or deny?