I struggled like crazy to get a good take-off, (I learned at 47) - Even though I could get up and surf I had some hitches in my technique that I knew held me back in fast pitching surf.
I have it dialed in now but it took awhile. It's not really an intuitive motion until you've been doing it awhile. Some people say dryland practice is a waste of time, but I don't think so - unless you can get in the water at least 3 or 4 times a week.
I do the same motion in dryland practice that I do in the water, but it feels much different in the water, and there are things that happen in the water that are crucial to getting right (push /lift of the wave/timing). But if you get get your body to automatically execute proper mechanics, then it's just a matter of getting the timing in the water. When you're older like myself you have to train your body in different ways than when you're 12.
Another big difference in the water is frame of mind. You've got to be determined to catch the wave. Don't underestimate this. When you're mind is focused on getting the wave, there are a lot of little subconscious movements that occur. You shift your body weight forward, you put in the extra paddle, your head leads your body - all without really thinking about it.
After an injury, I couldn't get into waves awhile and couldn't figure out what the problem was. Fear. Hesitation.
NO HESITATION!!! Major point.
Anyway, I don't think of it as an explosion or even a pop, but a tight, controlled lift and flick. "Flick" your legs forward and underneath you as the tail lifts and the nose drops. You can imagine how a dropping board would affect your mechanics, it makes it easier than on dry land. That takes water time to get the feeling.
If your pearling, you're on the right track, now you just have to get the mechanics together and get to your feet smoothly.
Here's a video I made for this forum.
https://www.youtube.com/watch?v=dFF4Pgxd2UAA couple things, I'm not sure if my hands are this far back when I'm in the water, because when my tail is lifted, my fulcrum point (my arms) moves forward slightly. Also, when I'm in the water my head is on a swivel right up until my last paddle or two when I put my head low to the board to get moving down the wave face.
Surf a lot and have fun - it will come. If you find yourself getting frustrated in the water just clear your mind and just enjoy yourself.
Hope this helps.