Just a few tips from Ponobill about punching through whitewater on your SUP. I’m not good at it. But that doesn’t keep me from trying! p.s. photo is a Sam Pa’e, whitewater puncher of the first water!
The key is that your legs don’t present much resistance to the wave, so basically you need to hump the board over. There’s a lot of stuff on this forum about it, I’d try the search function to look for it. 
Here’s my technique–some of it came from a casual comment by Randy (admin). As I’m approaching big whitewater I time my paddling so that I can give one last strong stroke just as the board hits the wave, and then reach up onto the wave and plant the paddle and pull. While that is going on you step back with your rear foot and preload the board, like doing an ollie on a skateboard. Then push the nose up. Be careful not to let the board come too high or it can smack you in the face. Been there, done that, got the lumpy forehead.
It takes practice, but you need to start working at it. You’ll never get better lying on the board.
You can go through MUCH bigger waves standing than you can lying down.