You can tell management that you're uncomfortable wearing used clothing. Don't expect them to work with you on this; no offense but most places in my experience which come with a required uniform do so because they can't be certain that a transient workforce will come in with work-appropriate wear and as such will very likely simply let you go and talk to the next person on their list of applicants, someone who likely does not have such a visceral reaction towards wearing "someone else's clothes".*
Or you could, you know, just deal with it. A big fat lot of us have had jobs in the past (often but not always early in our careers) where we had to make do with a uniform policy and all the attendant issues - not having access to new clothing, not being given enough changes of outfits to allow you to work 5 nights a week without either doing laundry several times a week or showing up with a stinky shirt, etc. I'm not saying this is good times to be had by all, but guess what? This is how the "other half" lives, so to speak. Given the tone of the original post, I think that you may benefit from this experience in ways you don't know right now.
This is not the place to ask legal advice but there are no statutes on the books that I have ever heard of. that state that a company must supply an employee with a brand new uniform. In fact, the reason I am almost positive that this is the case at least in the US is that what you're proposing would be a ridiculous law. There is a law that states that if a company demands a specific uniform for an employee, it has to provide it itself, but, yeah, not the same thing.
*Which, two things: one, as has been noted in the comments, a lot of people go to thrift shops to find used clothing. It's a perfectly reasonable thing to do, particularly if you don't have a lot of money. Frankly, there's an elitist streak to this question which is, I think, a big part of why it's been downvoted already. Second, even leaving the elistism aside for a second, you do realize that if you purchase all your clothes from a clothing store, the chances are high that someone has worn some article of clothing you currently own before you did, right?