If I'm writing it, here's my introduction of the Joker (This could also work in Gotham, but on principle it can't be done unless the show lasts 10 years).
We start with a guy we'll call Jack. He's somewhere between 25 and 30, only a year or two out of grad school, and recently hired as a chemist for a pharmaceutical company. Said PharmCo has recently released the most effective anti-depressant to date, available only in transdermal patch form. People are reporting dramatic improvements in mood and it is the only medication reliably effective against bipolar disorder. Of course, there are some down sides. Side effects include reduced melanin and brittle hair, teeth and nails. It's also dangerous if overdosed.
What Jack discovers is that only the slightest tick above the tolerated dose can lead to psychosis, dissociation and hysteria. PharmCo knows this, and this is why it is only released in a transdermal patch. Most accusations and lawsuits are quickly dismissed as the result of deliberate overdose, and even with all the lawyer fees PharmCo is still making money hand over fist.
So Jack decides to go all Edward Snowden on them and begins leaking documents to the media under the pseudonym "redhood". PharmCo catches him. What happens next depends on how much you want to stick with the (likely) canon origin of the Joker. The purer take would be for thugs to drown him in a vat of the drug and, believing him dead, toss him into the river. The take I like better is that they slap about 100 patches of the stuff onto his arms, legs and face until he goes cookoo and they then check him into Arkham, where his tales of evildoers in PharmCo will be seen as just another delusion. At first he still looks normal, but is catatonic. Then he screams for three straight days. Then the screaming suddenly transfers to laughter and within two weeks he has fully transitioned.
The drug is pulled from the market, but having worked on it himself the Joker easily synthesizes an even stronger formula and it becomes the famous Venom.