We get a sense of Arthur Fleck's (Phoenix's character before he becomes the Joker) social stature right off the bat when he's beaten up by some kids while he's just trying to do his job as a for-hire clown on the street (they also steal his sign and he gets in trouble for it by his boss). This moment kicks off a chain of events where he's continuously picked on and scoffed at.
As a result of the initial beatdown, one of Arthur's fellow clowns gives him a gun for protection. Not long after, three "Wall Street" guys give him grief on the subway late one night, and that's when he pulls the gun out and uses it for the first time, killing all three.
Another important thing to note about Arthur is his increasingly disturbed mental state, which only worsens after Gotham politicians decide to cut off funding to Arkham Asylum, which supplies him with access to therapy and medication. (His erratic laughing fits are a sort of mental tic, and it's implied they stem from some instance of childhood abuse.)