Well, they might not have as much animosity from the start. In the original, Snape had a lot of pent - up hatred towards James Potter which he transferred onto Harry. But if they meet before Hogwarts, Snape could see Harry as just a young boy in need of guidance rather than the son of his enemy. So, their relationship could start off more as a mentor - mentee, at least on Snape's side.
Their relationship could be more complex. Harry might see Snape as a bit of an enigma. Snape could be torn between his loyalty to Voldemort at that time (if the meeting occurs early enough) and his growing sense of obligation towards Harry. This could lead to a lot of internal conflict for Snape. And for Harry, he might be more understanding of Snape's later actions in Hogwarts because he had this prior connection. He might think there's more to Snape than just the mean professor he seems to be.
In this fanfiction scenario, Harry and Snape could form a sort of bond. Harry could look up to Snape in a way, seeing him as a powerful wizard. And Snape, instead of constantly berating Harry in class, might be a bit more lenient. This would change the whole dynamic in Hogwarts. The other students might be really confused as to why Snape treats Harry differently. And Snape might even secretly help Harry with some of his studies or magical problems before he gets to Hogwarts, which would make their relationship very different from the one in the original series.
Chapter 556, "Five-Year College Entrance Exam, Three-Year Simulation", is the clearest early answer because it turns Team's situation into a concrete plot event. It opens with After finally settling down, it wasn't long before Jiang Yan started...
Chapter 451, "Where Did This Madwoman Come From?", is the clearest early answer because it turns Jiang Yan's situation into a concrete plot event. It opens with Upon hearing this, the three people turned their heads in unison.
Chapter 504, "It's me, Gu Yu", is the clearest early answer because it turns Jin Siyue's situation into a concrete plot event. Early on, Just a short distance away, a group of people gradually approached.... By the end, You, who are you?" This question voiced the puzzlement of Gu Qiang....
Chapter 579, "I Know Where Team Q Is!", is the clearest early answer because it turns Team's situation into a concrete plot event. The chapter turns that into something concrete by moving from Young Master, what do you think?" Having finished reading the... to Yet Jiang Li said, "Is that so?.
Chapter 364, "This is the gift our master sends you for the first meeting", is the clearest early answer because it turns Shariputras's situation into a concrete plot event. A useful checkpoint is the way the scene starts with The final item is our heavyweight treasure for today." Even the host...
Chapter 242, "Jiang Yan's Dazzling Transformation Journey", is the clearest early answer because it pushes Dazzling Transformation Journey into a new phase or setting. It opens with Just when Jiang Yan called to heaven and earth in vain, he looked up...
Chapter 261, "They've Ruined the Entertainment Industry!", is the clearest early answer because it turns Shu Yan's situation into a concrete plot event. Early on, The village chief's eyes nearly popped out after he heard the whole.... By the end, Is it necessary to be so guarded against me?.
Chapter 568, "Not at All", is the clearest early answer because it turns All Shang Shaojing's situation into a concrete plot event.
Chapter 732, "Sister Xiao Wan, I Don't Understand", is the clearest early answer because it turns Jiang Cheng's situation into a concrete plot event. The chapter gives readers a real answer by opening on Bai Lu, eavesdropping in the corner, marveled at Jiang Cheng's...
Chapter 306, "I Believe Whatever Miss Jiang Says!", is the clearest early answer because it turns Jiang Li's situation into a concrete plot event. The chapter turns that into something concrete by moving from But Jiang Li seriously shook her head, "No, Aunt Zhou, this matter...