Yes, you can introduce a villain before a crime is committed. You don't need to use any clichés or tropes.
The essence of villainy is, in general, selfishness to the point of not caring about the welfare, life, or happiness of other people.
Over-The-Top villains may want to harm people for fun of it, be sadistic or enjoy the pain of other people, but that is not a necessary component. The central feature is the villain doesn't care , they don't necessarily like seeing people suffer, but if that's what it takes for them to get rich, get powerful, or see their project come to fruition -- So be it.
So a villainous bank robber may kill some guards or blow them up without a second thought, because she sees no other path to the money. The people are just obstacles to be removed, like the vault door. The same thing for witnesses, cops, or any good Samaritan that gets in her way. If she needs to shoot a driver to take their car, oh well, she pulls the trigger.
Yes, I am describing crimes, but more importantly I am describing an attitude.
If you show a banker that has a choice in whether to foreclose on a house, and knows she will bankrupt a family and make them homeless if she does, then forecloses anyway because she wants to make her bonus: She's a villain that has committed no crime, we know she's a villain because she chooses to ruin a family to make herself few bucks.
You can introduce your villain, as a villain, by having her choose to perform legal but heartless acts for entirely selfish reasons, even perhaps letting people die, because she doesn't want to get her shoes wet.
Turn off her sympathy. She doesn't have to be cruel, but she just doesn't do anything unless there is something in it for her, and not just somebody's gratitude for her being nice.
You can have her lie and intentionally deceive people without committing a legal fraud, you can show her for the predator she is, without committing any crime. You can allude to crimes she has been "adjacent" to in the past without explicitly telling the reader she was guilty. She can deny any guilt, and claim her adjacency was bad luck on her part. In fact, it couldn't have been her, because the guy claiming he got framed was found guilty, fair and square, by a jury, and died in prison, as he deserved.
The reader will know she is a villain, and be afraid for anyone interacting with her.