OP, yes you probably can get away with keeping it, but don't be a piece of shit. Contact them, see if they'll either send a return shipping label or let you return it to a store.
If they tell you to return it at your own expense, then I'd make a fuss and say no way its too heavy and too much of a hassle.
Maybe you'll get lucky and it'll be too much of a hassle for them and they'll tell you to keep it. That does happen sometimes, but I wouldn't just assume it, so unless they specifically tell you to keep it, contact them. Now if they don't respond (like if you sent a letter) or say they'll send you a shipping label and then don't, then I'd say ok as you did something to try to return it and its on them at that point.
Actually, how did you order it that they don't have your CC on file but shipped it to you? If they really wanted to (likely would not just because its too much of a hassle but some companies have done it over amounts that are ridiculously low), they could send you a bill and if you ignore that to collections since I'm assuming they have your name and address on file.
https://www.consumer.ftc.gov/articles/0181-unordered-merchandise
Q. Am I obligated to return or pay for merchandise I never ordered?
A. No. If you receive merchandise that you didn’t order, you have a legal right to keep it as a free gift.
Q. Must I notify the seller if I keep unordered merchandise without paying for it?
A. Although you have no legal obligation to notify the seller, you may write the seller and offer to return the merchandise, provided the seller pays for shipping and handling.
I think it's common for companies to write off mistakes; especially large companies.
I'm pretty sure that applies to stuff that you were sent unsolicited (as in you did not order it). This used to be a huge scam, where companies would send you an item and then later on would bill you if you didn't send it back, even though you never ordered it in the first place. People thought it was free stuff (and some of the companies acted like it was, but it either had other stipulations like you had to order other stuff or something, or was said in fine print "return if you do not want to be billed") and would keep it not knowing what was actually happening. The FTC had to crack down on it.
I'm fairly sure this does not apply when they just send you the wrong or defective item. There is some gray area, but generally you are expected to return the incorrect item when you've received the correct one.
You got what you ordered and paid for, but not in the time frame you expected. In addition to this, you got something you didn't order and can keep it. At least that is the way I look at it.
Honestly, unless it is an expensive item Target may look at it as more of a loss to take back and sell open-box than to let you keep it for free.
That's not really what that is though. A simple mistake if very different from receiving something you never ordered.