If you want to train your Pug scientifically to catch a Frisbee, you need some targeted exercises. The younger the dog is, the easier training usually becomes. Puppies tend to learn faster, accept new things more readily, and show stronger obedience, so early work is especially helpful.
The first step is obedience training.

If you want your Pug to learn the Frisbee game quickly, it first has to understand commands such as "bite" and "drop." In fact, Frisbee training is really a game played together by the owner and the dog. The owner's task is to gradually increase the dog's interest and make the bite-and-release parts of the game smoother and faster.
The second step is practicing with rolling objects on the ground.
This means letting the Frisbee roll along the ground while the Pug learns to bite it and bring it along. Because the difficulty is lower, this helps the dog get used to biting a moving target. It is an excellent foundation for later Frisbee-catching practice.

The third step is teaching the dog to use its body for takeoff.
To catch a Frisbee in the air, a dog needs a certain degree of jumping ability. Owners can therefore start by training the hind legs, teaching the Pug to push off strongly so that it can jump upward more effectively when the Frisbee is finally thrown.
The fourth step is training the dog to catch the Frisbee in the air.
By the time the earlier groundwork is done, the air catch becomes much more natural and not nearly as difficult. At that stage, the main change is simply gradually increasing the throwing height and distance.
The fifth step is reaction-speed training.

The owner can use several Frisbees in sequence so the dog practices biting, jumping, and dropping repeatedly. During this process, the pace can slowly be increased.
Throughout all of this, the owner must carefully control the Pug's excitement level. When the dog successfully bites the Frisbee, it often becomes very excited. At that point, you should let it enjoy the Frisbee for a moment, then take it back and start again. This back-and-forth creates a strong sense of fun and interaction.
If the Pug becomes too excited, let it calm down for a while or have it run around more. If possible, it is even better to let two people throw in turns so the dog runs back and forth. That both tires the dog pleasantly and keeps it very happy.