The wave itself is a shock wave and is moving through the water. The faster you can paddle, the less chance you have of getting caught on the inside. To build speed, make sure you are far enough forward on the board so as to get maximum flotation. The nose of the board should be just above the water line when at rest. Also, make a cup shape with your hands, keep your fingers together and your wrist stiff so you will have maximum pull with each stroke.
Fitness training is the best way to make paddling easier.
I recommend weight training focusing on upper arm strength. You also need to have good endurance which comes with aerobic exercise like, running, mountain biking, etc. When paddling out, be aware of other surfers in the water and do not paddle directly behind them.