Would you ask for a refund?

Let’s say you adopt a puppy from Craigslist with a rehoming fee of $380. The ad claims the puppy is 7 weeks old with first shots (you also have a picture of the ad that make these claims). You go to meet with the seller (you have his number and address as well as text messages about the transaction that’s about to take place) and he brings out what’s rest of his litter 2 males and 1 female (seller had five puppies pictured on his ad). You pick out a male and take him home, you give him water and soft puppy food. After closer inspection you realize he doesn’t have any teeth which means he’s much younger than the seller said, he’s about 4 weeks old (you’re worried but you’ve nursed and raised a puppy that was between 2-4 weeks with little to no problem, she is now 1 year old and in good health). You buy two different formulas for young puppies, you buy a nursing kit, a syringe, and two different kinds of puppy food (kibble and soft), you do as much research as you can to refresh your memory on how to care for such a young pup. You do everything you can for this puppy, you can’t take him to the vet because your pet insurance doesn’t cover puppies under 7 weeks. You have the puppy for a week and it passes away, would you ask for a full/partial refund under false advertisement (since the poster said the puppy was 7 weeks)? Is the buyer at fault, is there not much to be done since you don’t have a receipt or “proof of purchase”?