I wouldn’t recommend using pre-ground coffee, because making cold brew works best with very coarsely ground coffee (like for French press) and most pre-ground coffee is finer than that. If you don’t want to grind your own, see if you can get it ground for French press.
As for filtering out the grounds, you can put the grounds into a big filter (they sell them for tea). And then there’s this if you want to take your game to the next level: https://toddycafe.com/product/toddy-artisan. I got it as a gift, and it works very well.
