Unfortunately every time you give in you are encouraging her crying later.
The first thing to understand is that your puppy has probably never been alone before so her anxiety about that is expressed as crying or whining. Usually that will improve noticeably in less than a week if you approach it correctly. Any time you go back to her area while she is crying you are encouraging that behavior. Even an "it's okay" or "shhhh" is rewarding her whining. You have to ignore the crying and not go back until she has been quiet for at least 30 minutes or after she wakes up. Other steps you can take that may help is using a covered cage (it will still take several days to adapt), having the cage in an area where she does not see or hear you and using interactive chew toys such as Starmark Everlasting Treat, Kong Quest or Traxx, Nylabone Romp n Chomp or processed bones or antlers (Blue Buffalo). Having music or a ticking clock can also help. The most reliable solution is a second puppy but if that is not feasible try these other suggestions.
Your puppy likely has spent plenty of time in a cage or other enclosure, but she probably was not alone. It is important to understand that she doesn't hate the cage, she hates being away from you or your family. Her mindset at this age is similar to a child at 3 years of age. You have to enforce a routine that includes rest periods and then she will adjust and accept that with time. Have the cage in an area separate but near, use a cage cover and once you place her in walk away and do not go back.