Why don’t vaccines cause autism?

Just to preface, I am not an antivaxer but just interested in the science side of this topic. I understand that the original study that “found” the link between the mmr vaccine and autism was very flawed and later retracted. I also know that there is not rlly a single, definitive cause for autism but I’ve seen some studies that show a link between brain inflammation in children and autism (uni of Mariland, Autism Research Institute, John’s Hopkins university) (sorry idk how to insert links). One of the potential (rare) side effects of vaccines is brain inflammation so couldn’t that possibly cause autism?