How would things be turn out in Toy Story 1 if Buzz Lightyear didn't see his commercial that made him realize that he was actually just a toy to begin with? What if Buzz still thought he was an actual space ranger?
Woody accidentally woke Scud up with his pull string, and he and Buzz split up. Once Scud walks away from Buzz who was hiding in Sid's Dad's room, he noticed a commercial playing, and this is where things change.
Instead of the Buzz Lightyear commercial playing, it would just be a different commercial of any kind you can think of, or a show playing. Later on, Woody comes out of the closet, telling Buzz that the coast is clear, and asks where is he.
Woody noticed the TV playing and went to investigate, and there he is, eyes glued to the TV. Woody tells Buzz they have to get out of Sid's house before Sid could torture them more, and for the first time since he noticed the TV playing, Buzz took his eyes off the TV and asked Woody if he had any ideas.
Woody then realized that Andy and Sid are next-door neighbors, so possibly, the windows of Andy and Sid's rooms are connected to each other. Woody and Buzz rushed out the room without being detected by humans, and grabbed the Christmas lights and rushed over to Sid's room.
Woody and Buzz hurried to the window, Woody opened it, and called out for the toys that are in Andy's room. At first, they didn't bother, since they still thought Woody murdered Buzz, but when they saw that Buzz was with him, they opened the window and apologized to Woody for accusing him of murder.
Woody explains to the toys that he and Buzz been toynapped by Sid, and that they need to go through Andy's window before Sid or Scud could catch them. Woody throws out the long Christmas lights which Slinky caught, and Woody taped it to the table, and now all they had to do was climb over to Andy's window.
They eventually made it back to Andy's and Woody finally realized that he has been too harsh on Buzz, so Woody apologizes to the toys for knocking Buzz out the window, and they all moved to the new house.
Although, without Woody and the mutated toys coming to life in front of Sid, he would continue torturing toys for fun, and I don't think he would become a garbage guy, and that's that for Sid.
But when would Buzz start thinking he's actually a toy in this timeline? Time would tell. And what about Toy Story 2?
Well, Andy would still rip Woody's arm by accident, and Al would still steal Woody to complete his Woody's Roundup collection to sell to Japan. However, for Buzz, he would probably befriend the Utility Belt Buzz, and for Woody, he would probably go to Japan without Buzz convincing him that going isn't worth it.
Now, for Toy Story 3, they'd be stuck in that attic since Andy doesn't have Woody and he would quickly pack up the toys in a garbage bag and bring them to the attic before Molly would ask Andy for help. And Toy Story 4 wouldn't be a thing at all. And that wraps up the scenario.
