The first major event in the novel comes when Montag meets Clarisse; her unconventional words and thoughts spur real thinking in him, making him wonder about his role in life. Montag begins to wonder how a person like Clarisse can be so different, and yet he feels a deep connection with her.
The second major event comes as Montag returns home from work; he finds his wife Mildred passed out on the floor from a pill overdose and calls emergency services. He wonders if it was intentional, and if so, why; what is it about her life, seemingly so perfect, that caused her to try and commit suicide? This event, along with the first, breaks Montag from his placid conformity.
A third major event comes when Montag goes to burn a houseful of books; the women inside refuses to leave, and rather than submit to the government-sanctioned burning, lights a match and burns herself along with the books:
The woman on the porch reached out with contempt for them all, and struck the kitchen match against the railing.
(Bradbury, Fahrenheit 451, Google Books)
This so disturbs Montag's view of his life that he becomes ill; with that, he becomes detached from society's norms and starts to rebel in earnest, showing his books to Mildred and reading aloud to guests.
There are quite a few other major events, but these three early events are the most important in setting the stage and starting the rising action of the novel.