I used to work at a very large, very well-known tech company, the cool kind with the coffee bar downstairs, and the pool tables, and whatnot. The company had an open office plan, which meant no high cubicle walls, and very few places to get away from the constant background noise of hundreds of people talking and typing.
The solution? Wear headphones. Everyone did, especially the developers who were trying to focus and get work done. There was no other option.
But let's say your coworker's notifications are so loud that you can hear them even through whatever background noise you've got going through your headphones. In that case, you're probably not the only one who is annoyed.
Yes, you can confront your coworker directly. However, it's not unreasonable to go to your manager, and explain the problem:
Hey Lisa, I need to ask your advice. I'm trying to do my work, but it's just so loud I can't concentrate. Is this normal? I'm wearing headphones with the music turned up, but I can still hear most of the racket in the office. There's people talking and phones going off really loud every few minutes and all kinds of distraction. I just don't know how I'm supposed to be effective in this environment. What can I do?
In an ideal world, your manager will send out an email asking people to keep the noise level down, and you'll get voluntary compliance from everyone, including your offending coworker.
Also, after you get some support from your manager, it should be easier to go to your coworker and remind them of the policy:
Hey Frank, man, could you turn down the volume on your devices? I can hear them even through my headphones. Thanks!