Oh, we always have people come into our theatre company with no experience. Some act, some go into tech, and everybody seems to have fun.
If you're interested in costumes, I'd suggest going to help out with quickchanges, or just organizing them, at first, unless you actually know how to sew some. Then alterations, creating costumes- even small pieces like hats are a big help. A lot of costumes work is just finding the stuff, too, in thrift stores, or online, or by word of mouth from people's closets.
Props is ridiculously easy to get into, because nobody wants to do it. I will tell you this because I made the mistake:
If you have no experience in props, and someone asks you to head props, say FUCK NOOOOO. Seriously. So much stress.
Usually there's a props crew, though, and they always need lots of help, with finding things, building things- and depending on the show, it could be anything. I can personally say that I've had to decorate Christmas trees, build giant foam sandwiches, find an inflatable Loch Ness Monster, and learn how to make a rat vibrate, all for props.
Sets are fun to get into, too, but wouldn't do you much good for cosplay. Things always need to be painted and built, though, and as long as you can hold a brush or a hammer, they'll usually take you on.
Then there's the tech run side of things, like lighting, sound, and stage management, but I don't recommend jumping into those until you have more experience.
Best place to start, in my opinion, though, is running crew. One of the actors not on deck? Running crew goes to get them. Champagne bottle needs to be filled for the second act? Running crew fills it. Actress's flashlight needs to be on the other side of the stage? Running crew takes it there.
Simplest jobs, but absolutely essential, and a great place to start. You get to watch everything going on around you, and still be a part of it.