I grew up watching Soviet movies about war, which usually depict very different picture. Sure, there are heroes, but they are not super heroes as in American movies. They get injured, die. Soviet war movies show that wars really suck.

Some UK war movies fall into the "wars really suck" category - an obvious example being The Cruel Sea based on the novel by Nicholas Monsarrat who served in Royal Navy during the Battle of the Atlantic:

"This is a story of the Battle of the Atlantic, the story of the ocean, two ships, and a handful of men. The men are the heroes; the heroines the ships. The only villain is the sea, the cruel sea that man has made more cruel."

In my experience, other countries don't view themselves that way, and it's mostly seen as an Americanism (I'm not American)

Long time ago I heard this joke: Ship is sinking, the captain needs to tell everybody 'women and children first' . So to the british: you are gentlemen, aren't you? To japanese passengers: look what everybody else is doing. To US-American: you guys want to be heros?

Maybe to a lesser extent but you can find Indian movies of absurd heroism too. That's what propped me to think America is not very special.

Also being a young and rich state probably pushed things to eleven.

I wouldn't say "being young" is that relevant after a couple centuries. Nobody in the US today knows someone who witnessed the declaration of independence (unlike, say, in Israel or India).

Probably. But I believe there's still a notion that they're new players who got everything right to the top. While other countries have seen peaks and valleys.

That is also true for the police. Usually the police is incompetent if you want to be funny, or they are suffering humans. The police as a hero is also USA propaganda.

British war films made 1939-1945 were explicitly propaganda. And there was a lot of them.