In Toy Story, it makes no sense how Buzz was able to realise he was a toy after seeing the ad, but couldn't realise before.

It seems like before he saw the ad, he simply didn't have the ability to realise, regardless of the evidence, but then he suddenly gained the ability. Before he saw the ad, there was lots of evidence that was much more obvious, that he simply dismissed, such as the fact that his spaceship was clearly made of cardboard. So if he could dismiss all the other evidence, he easily could've dismissed the ad. He even could've come up with somewhat logical ways to justify it, e.g. "I'm the real Buzz Lightyear, that ad is for an action figure based on me".