If Hermione had gone to Harry first in Prisoner of Azkaban, the biggest difference might have been how quickly the trio resolved their conflicts. When Harry received the Firebolt, Hermione reported her suspicions to Professor McGonagall because she feared Sirius Black might have sent Harry a cursed broom. Harry and Ron both turned against her, feeling she had ruined Harry’s Christmas present. Later, when Scabbers disappeared, Ron blamed Crookshanks, and Harry initially sided with Ron. If Hermione had approached Harry first and explained her concerns more openly, he might have been more willing to hear her out instead of treating her actions as betrayal. But Harry was stubborn, and his excitement about the Firebolt made him reluctant to consider that Hermione might be right. The bigger question is whether Harry would have believed Hermione about Sirius and Scabbers sooner. Hermione was often the one who thought through the evidence, while Harry tended to act on emotion, especially when it came to his parents and Sirius. If she had spoken to Harry first, he might have trusted her reasoning earlier, potentially changing how they approached the mystery. However, the book gives no reason to believe that a different conversation alone would have exposed Peter Pettigrew: the truth only became clear when the trio followed the dog into the Whomping Willow’s passage and confronted Sirius and Lupin. So the most credible answer is that Hermione approaching Harry first could have improved their communication, but it probably wouldn’t have changed the central events unless Harry was willing to listen and reconsider his assumptions.