Is it possible to introduce evil characters (be identified as evil) before the action (the crimes committed by the characters) takes place?
Happens all the time. It's a staple in many a superhero movie where the villain is typically motivated by pure means until he or she gets their powers. Doctor Octopus and Green Goblin both got scenes with Peter Parker where they were fatherly to him before they started their villainy. In the comics, Doctor Kurt Connors is a traditional ally of Peter Parker, even though we all know Spider-man will have to fight him as the lizard (the Toby MacGuire films never introduced the Lizard, having been seen in all three films with his motivation in place. It was likely he would have been in the fourth film if there was no reboot). Doctor Strange features Baron Mordo, his traditional archenemy as an ally and teacher who only turns at the end of the film, setting up a sequel antagonist.
Disney's Frozen goes to great lengths to hide the villain of the work until his big reveal in the beginning of the third act and we're led to believe he's a stand up guy. Scar's introduction is Mufasa berating him for not being at the presentation of his nephew. While he's understandably a jerk, it's a social faux pas and not an actual crime. Scar's first real crime, regicide comes much later in the film, and he does act like a silly uncle to Simba up until that point.
One notable film, the 5th element, goes the whole film without the villain and hero meeting face to face. This was done in a bit of an homage to Bruce Willis' previous film, Die Hard, where the writers realized that Willis' heroic character never met the bad guy until the climax of the film and wrote a scene so they met much earlier.
Crime Fiction, especially whodunnits and mysteries, work on the premise of leaving clues for the identity of the villain for the audience to work through with the characters and see if they can pin the crime correctly. This involves multiple suspects and careful wording as the villain usually gives themselves away by saying or doing something that doesn't fit the story, usually so innocuous that it can easily be missed.
The First Harry Potter Book is another interesting scenario, in that the heroes figure out the villain's plot but they pin it to the wrong character up until the final confrontation. The second book did something similar. The third had the villain frame someone for the crime and revealed the villain to be a character who was introduced in the first book and was rather unassuming. The fourth book played around with this as well, and the final 3 the villain was pretty much the people you suspected, though the sixth book gets a little mention as the villains were both Red Herring characters in previous books so no one thought they were actually up to shady shenanigans until it was too late.
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.
I understand your question as asking: is it possible for the reader to know that a certain character is evil, from that character's introduction, and before that character actually commits any evil acts?
This precludes having the character commit some crime that is unrelated to the main action, so that we recognise their evil. It also means it is irrelevant to consider things like plot twists and red herrings, because we want the reader to know that the character is evil, we just don't want to make her do anything evil yet. You're also not looking for an answer like "you have to foreshadow it" because the question is how do we foreshadow, or rather clearly signal, that the character is evil. Finally, it's not even about characterisation: you're not asking how to let the reader know the character is nasty, as the trait you want to convey is evil. (This last assumption is perhaps the least necessary one; perhaps you don't need to immediately convey the evil of your villain, but can show us she is a vile person with the capacity for evil; but I don't think that's the question, so I won't go into it here.)
I'm also assuming you don't simply "tell" us she is evil (e.g. an omniscient narrator saying "people liked her, but actually she had a wicked heart"), or "show" us in a way that is just a trivial shortcut: " 'man, I haven't killed anybody yet, but I'd love to murder a bunch of people if I could get away with it,' she thought".
The main solution I can think of involves tropes and cliches. Now, this may sound bad, and often we talk about tropes and cliches being used badly; however, sometimes, they are, simply, signalling mechanisms that a storyteller can use in order to signal certain ideas to her audience.
A classic example is the "kick a puppy" trope. Now, don't get me wrong, kicking a puppy is a vile thing to do. But if we're talking about e.g. some uber-powerful arch-mage who can wipe out a city with a storm of fire, or some military top-brass guy who can, well, do the same thing--and the story does, in fact, involve the possibility or actuality of crimes on that scale--then kicking a puppy is not on the same scale as the main crimes that will make the character evil. So, we show the character kick a puppy, and (for a modern, western audience at least; I don't necessarily know about other groups) we instantly know this character is a horrifyingly evil monster. "What sort of person would kick a puppy for fun???? And this guy controls nukes???!! Aaaaargh! We're in trouble!" Of course, we can play with any number of tropes or cliches to get the same effect. If you're writing in America you might get the same effect simply by making the character a communist, and if you were writing in the Soviet Union you could simply have made her a capitalist.
It's certainly possible, but it's not always easy to do in a way that doesn't feel forced. If you look at it from the perspective that "evil" is more of an attitude than a specific act you can show that the character might possess that attitude in various ways:
Have something happen that they react to in a way that an "evil" character would rather than a "good" one:
Pete slipped, crying out in pain as he hit the ice hard, the snap of bone breaking sounded like a gunshot. Megan and Rob rushed immediately to the fallen boy. Sue, who had been walking a few steps behind Pete simply stepped around the small throng, "Enjoy your trip fatty?" she sneered. Then immediately let out a braying laugh at her own joke.
At this point Sue hasn't done anything evil, she didn't push Pete over or anything - but most people are probably going to identify that not only not stopping to help someone in the group who is obviously hurt but actually mocking them means that Sue is probably not a good person. Later on you could have Sue actively do something "evil" and it would feel natural to the reader - you've already established that she isn't a hero.
Evil people are going to think about their evil deeds before they do them, so if your structure supports having them as a POV character, even if only for a brief glimpse you can show this:
Steve felt the bile rise in his throat. They sickened him, all of them, with their incessant chattering, and giggling. He slipped his hand into his satchel, feeling the cold, hard steel of the pistol, caressing it. Soon he thought, Soon.
Again, our "evil" character hasn't actually done anything yet. But you can see that he's not only thinking about it but that he intends to do it. You could now cut away from Steve's POV and have the plot do other things for a while before having Evil Steve do his thing.