Some days I can barely even get started working, because I am already anticipating interruption.
Wearing headphones doesn't help. I think it should be a clear social signal, but other people do not. In fact, they talk to me as if I can hear them (I cannot) and have to repeat whatever their introduction sentence was when I finally take them off.
Why is this normal?
One way to do this would be to buy (e.g) a bunch of white caps and tell your coworkers to wear them when they need to concentrate, and to not disturb others when they are wearing them. I know of at least one company that does this and it works well for them. You can also do this with headphones, just tell your coworkers politely.