I watched gym athletes fail this test for years. Bench press doesn't carry a high-rise pack up four flights.
The CPAT is eight specific events done in sequence under a 50 lb vest. Train the events: stairs under load, sled drags, farmer's carries, grip work. If your workout doesn't leave your legs and grip smoked, it's not CPAT training.
What's your current training setup — gym, garage, or bodyweight? Post it and I'll tell you what to add.