This can only be done in movies or comics, something with visuals. But I noticed that they have a character, and they put things in their room or somewhere else so that the watcher can infer character traits without making it forced. They do this a lot in the 'The Royal Tenenbaums'; because the book it was based off of went into more detail then the movie could on each character. The director decided to just make their room show their personality's. I also noticed this in 'The Amazing Spider-Man', they show a few things Peter engineered himself, and it lead to him making web shooters without going into all the science and everything. I liked that, but wondered is their more methods like this in story telling where the watched can infer things?
You're asking if you can show traits through the characters' possessions, activities, etc.? Sure. Also clothing, body language, the way they speak. If you look at French realist novelists, like Balzac or Flaubert, they did a lot of this. It can mean a lot of description, which some people don't enjoy, but I think if you keep it to a few well-chosen and relevant objects/physical traits it works well.
Of course, you can put that in writing. I do it often myself. Something that helps me is to determine some of my character's quirks, and then develop items or possessions that provide evidence of those quirks. For example, if my protagonist is a environmentalist, I would write in a description of the "FUR IS MURDER" poster on his bedroom wall and make reference to the university diploma in "Urban Planning" framed in glass. In fact, I wouldn't need to even mention my character being an environmentalist after that. Start with the characteristic that you'd like to show off. Then, come up with a list of things that can have something to do with that characteristic. After that, make a few creative choices and show them off.
The above posters are correct. How they speak, walk, think and act sends a lot of messages to the reader. You don't always have to have your character giving out a first person thought every five seconds for that to occur. Just let your MC interact with others and it'll allow you to describe/infer things about without having to do an info dump however small or large.
I don't really mean character traits, these things are a given. I meant like how Peter has a thing to automatically lock his door, in a way foreshadows the web shooters being made. I mean things like that, for the story to move forward.
Foreshadowing, red herrings, Chekhov's gun, etc are literary devices used in plots. Storytelling is not just about writing a story that lays everything out in front of you. Storytelling involves weaving plots that have subplots. Some writers may mention an object once in a story and then not even mention it again until the climax of the story, where we suddenly find out exactly how important that object was to the core of the story. Because books are not movies, you can't "show" a few things sitting on a counter than a character engineered. You have to describe it. It is perfectly acceptable to have characters have various gadgets laying around only later to have that character invent something useful and/or important. How much "science" you do or don't go into is left up to the writer. Because I'm not really sure if I've satisfactorily answered your question, I'll make this suggestion. There are quite a few books that have been turned into movies. I suggest picking one and reading the book. When you're done, watch the movie. Then compare and contrast the way inference/foreshadowing was handled in the movie vs. the book.