Yes, they exist. Take a look around. Is the place dirty, crowded, disorganized? Look at where the employees are taking meals. Chances are it's a folding table in the middle of the factory. If there's not a dedicated space for employees to take a break, it's a sweatshop. If drinking water isn't provided, it's a sweatshop. If you venture into the restroom and quickly turn around, it's a sweatshop.
Is the pricing they are offering significantly lower than the competition? If so, they are probably offering these prices on the backs of their employees. There's no magic to apparel production. It's hard work, a lot of moving parts and it requires a massive amount of organization. Sure, there are the rare instances of the company that can offer lower pricing as a result of successful implementation of lean manufacturing or an otherwise superior workflow, but, if the place doesn't appear organized, efficient and advanced, then it's not.
There's no one definition of what constitutes a sweatshop. You'll have to be the judge. But if it looks the part, it probably is.