Yes, puppies can grow out of separation anxiety with proper training and positive reinforcement. It might take a few weeks to months to train them.
Why Do Puppies Get Separation Anxiety?
Puppies suffer from separation anxiety as they are always dependent on others.
Everything seems to be different and frightening, although you, being their parent, are the only consistency, so they have nothing else to go to, and that leads to attachment.
Usually, small puppies have not ever spent considerable time away from their family; they lived the initial 8 weeks of their lifespan with their moms, brothers, and sisters before actually living with you.
That said, being by themselves is an unfamiliar environment for them.
Canines can become irritated and frightened whenever they are confused or not provided enough exercise.
It is much harder with small puppies since they have lots of enthusiasm, and it is difficult to burn all of it without tiring them. 
Did you Know?
Separation anxiety is sometimes exacerbated by under-stimulation
Is Separation Anxiety Normal in Puppies?
Usually, pups will experience some panic when left by themselves in the beginning, but that is normal and would pass with time.
A little anxiousness, on the other hand, is not at all like complete separation anxiety, which would be problematic and needs medical attention.
But, it is quite apparent, with approximately 14% of canines in the United States suffering from it. 
Will My Pup Grow Out of Separation Anxiety?
Unfortunately, if you do not address the signs of separation anxiety as soon as possible, they will escalate.
Pups would not magically get treated with separation anxiety while they develop their bodies since it has nothing to do with their growing stage.
If a canine is left unattended from the beginning and does not ever get used to feeling secure with its own company, it would not be possible to form a good connection with you leaving the house. 
You must be a good canine owner and put every effort to guarantee that you grow an emotionally strong and fearless pet because your pets are unable to communicate with you and show you what they want and things they could feel.
Puppies, despite their small size, are unable to cause serious harm but think about what they might do after they are fully matured and struggling with a higher level of stress as a result of your failure to change the behavior.
Consequently, you would be coping with a completely different situation!
Did you Know?
Most shelter dogs suffer from severe separation anxiety as a result of past mistreatment
Which Puppies Get Separation Anxiety?
Separation anxiety may affect any furry friend, but it is particularly prevalent in animals with lots of stamina, intellect, powerful temperament, and greater social demands since they demand somewhat more engagement than other canines.
The biggest attackers are Border Collies and Labrador Retrievers. Vizslas, for example, are inherently clingier than some other dogs. 
How to Do Separation Training with Your Puppy?
Separation anxiety in pups can be avoided or reduced by slowly increasing their liberty and establishing positive connections by separation training.
You may accomplish this by gradually increasing personal time.
To begin with, walk out of the home for a short period of time, such as 5-10 minutes.
Take the initiative of not making a big issue when you leave since this might exacerbate anxiety.
Rather, once you return, create a positive environment and make them believe that they will always have warm hugs or long cuddle time whenever you step out of the home.
The second morning, go for a little longer and gradually increase your leaving duration.
It creates confidence in your pet that you would always return.
Promote solo playtime using a treat vending machine to create a good connection with their alone time.
Then, if it is appropriate in doing so, consider leaving your dog with his favorite toy whenever you walk out.
Not just playing would be entertaining, pass the day, and keep their thoughts occupied, but gnawing and having fun with different objects are also excellent stress killers for canines.
Habituating your dog to specific separation cues is also a wise decision.
If your canine is mature enough to understand routines and predict your behaviors, consider executing something like grabbing house keys and shoes and preparing your bag that you will typically do when going out for work.
Rather than going out, sit on the couch and watch TV or cuddle with your dog.
It demonstrates to your pup that your behaviors are not a cause for concern, and it may alleviate some of their anticipated stress. 
If your pooch suffers from extreme anxiety, you may want to consider trying an anti-anxiety dog medication.
Many puppy parents believe that offering their pet an item with a pulse is therapeutic.
They minimize anxiety by simulating being around siblings.
Anti-anxiety pills and plug-in humidifiers with organic calming substances such as CBD and aromatherapy are also popular. 
How Long Does Separation Training Take?
The amount of time it takes to train your pet with separation anxiety is determined by the level of his or her fear.
But, if you practice something each day for a few weeks, you might notice an improvement in your dog’s anxiety issues.
Separation anxiety in puppies could be difficult to control, and it is a painful condition to witness.
Gradually introducing your puppy to alone time might make a huge difference with this separation anxiety.
Try leaving your home and assure your pet that it is going to be more fun when you return home.
Start with 5-10 minutes and slowly increase the time while leaving him alone with its beloved toys and other entertaining things.