You know the nature of my work puts me in the position of giving feedback on students' photography.
And there is a funny phenomenon. There is a typical answer that always comes back when you ask why the photographer didn't do something - recompose, or try another angle- and that answer is always the same: “It all happened too fast, I had no time to respond,” or “I had time only for this one shot, and that's why I couldn't get a better one.”
And while it might sound like a valid reason, one many of us can identify with, the real reason underneath it is that the photographer wasn't ready.
Something happened just next to him, but his mind was busy with something else, and he didn't have the time to take the extra step, to move aside for better framing, or to put the focus point on the subject - and instead he nails the background in focus.
And why is that? Wasn't he standing at that place? Wasn't his eye open? Didn't he hold the camera in his hands?
Why do we catch the moments in their last moment?

THE SINGLE-POINTED MIND
The reason for that is the single-pointedness of the mind. The mind can know only one thing at a time. We often think that we are multitasking, but that's far from the truth. We are just jumping quickly from task to task.
So when that moment was happening near us, our mind was simply occupied with some other task. And that can be anything. You can stand there with your eyes wide open, thinking that you are looking at the scene and searching for moments. But in the back of your mind, you might be thinking about something that happened to you earlier at work, about a conversation you had, or just running through your to-do list: I'm going to do this and that.
Our minds are rarely in the moment. They are always processing something, always busy doing something. They are rarely 100% on the task we have assigned to them. Like photography :))
We can blame social media, phones, or anything else, but the truth is that we today are much less focused than we were 20-30 years ago.
This is really the same idea behind what actually improves your photography: it always comes back to attention, not gear. I've written about that here.
But there is a way. Even two ways.
THE FIRST WAY: MEDITATION
The first one is to train the mind to stay with one mission for extended periods of time, and you can do that through meditation. The first step in most meditation techniques is to concentrate the mind, and it's done by trying to keep the mind on a single meditation object for as long as possible. That develops the single-pointed concentration that we need so much.

THE SECOND WAY: LONGER SESSIONS
But let's say meditation is not something for you — there is another technique. I'm pretty sure I've mentioned it in some of my videos, but I'll share it with you here too.
The second method is much easier. Just do longer sessions of photography. At first you will be distracted, but as the session continues, you become more and more submerged in the process. The important part is to try and do it alone, with the phone in your bag, and just focus on photography — searching for moments, for textures, colors, light... anything that turns on your photographic excitement.
Actually, this is also a sort of meditation. Just here, we are making the process of photography itself our object of meditation.
That last one is known to many great photographers. Some even say that real photography starts after two hours. Try it, see how you feel.

WHAT CHANGES WHEN YOU GET THERE
When you learn to be completely submerged in the process, nothing jumps on you and nothing surprises you. You anticipate.
Moments don't jump on you anymore. You see things develop, and when they climax, you are ready. So that problem you have with being surprised is solved simply by getting your mind straight.
Hope it was useful.
Happy shooting!