The documentaries on Vasili Arkhipov and Stanislav Petrov. Aptly, and despite being unrelated productions, both documentaries have the exact same title: The Man Who Saved the World.

Spoilers for Unsong:

I think quite a few titles from this ranked list of all EA-relevant documentaries, movies, and TV series I've watched might be interesting to you! :)

I am imagining movies with heroes where it wasn't their job (so not the soldier in 1917 / most war movies) or they weren't in some sense "chosen" (most superhero / fantasy movies). 

Seven samurai: where some samurai reluctantly attempt to protect a village. 

Princess mononoke: I just think this is a good hero story. 

Hacksaw Ridge (I didn't really want to include any war movies, but I think this merits inclusion because it's  about a conscientious objector. Very violent.)

Haven't seen Hotel Rwanda but it may merit inclusion. 

Spoilers for Avatar: The Last Airbender:

• Zuko's decision to join Team Avatar and warn them about Fire Lord Ozai's plan to destroy the Earth Kingdom may have saved millions of Earth Kingdom citizens.
• Aang figuring out how to defeat the Fire Lord:
  • When Aang ran off during Parts 1-2 of "Sozin's Comet," he consulted the previous 4 Avatars about the moral dilemma he was facing: how to defeat Ozai without killing him. As a fellow Air Nomad, Avatar Yangchen shared Aang's belief in the sanctity of life, but persuaded him that as the Avatar, he needed to put the world first. So initially, Aang concluded that he had no choice but to kill the Fire Lord.
  • Later, Aang was about to kill Ozai but decided against it because he had a better alternative. A lion turtle had given him the power of energybending, which he used to defeat Ozai by taking away his firebending ability instead of his life.
  • At both points, Aang made the correct utilitarian decision given his abilities and knowledge at the time.

Two examples come to mind:

• La vita è bella, a movie wherein the occupants of a concentration camp collaborate to help a child. It's not a movie about saving many people... but I'd say it involves altruism and self-sacrifice.
• Speaker for the dead (Ender's game series part 2), wherein the protagonists encounter two alien species and figure out a way to live together. This one does qualify as saving many  "people", but it's less purely altruistic. Bonus: There is a cool AI in a key role ;-)

I think Asimov’s Foundation is a great example of this! It features the establishment of a space colony with the goal of drastically reducing the length of an age of galactic barbarism, and ways that select inhabitants very cleverly manage to help this colony survive against various threats.

I feel like a decent percentage of protagonists in Participant-produced movies/TV shows would fit the bill here. 

Gravity's Rainbow probably also would be an example of this, as it basically (/supposedly?) is the story of de-risking of V2 rockets during WWII, and is written on an insanely-big scale (400 named characters, over way-too-many pages). However, I gave up on reading it after a few-hundred pages, because it is very long, VERY postmodern, and practically requires a string map to follow - so I don't know if the remaining 75% of the book suddenly shifts gear and portrays the Nazis as the good guys. 

(please note: this is slightly facetious in tone)

I would say Harry Potter is not exactly an EA example. The super-powerful almost-immortal physical embodiment of evil has a huge beef with him (a not-very-skilled not-very-smart teenager??). Though he knows that Evil Embodied is constantly trying to assassinate him in inefficient baroque ways, Harry Potter puts hundreds of other wizards in danger (resulting in a few dozen deaths) by going to Hogwarts versus, eg, insisting on homeschooling. Why is Harry the sole person who can save the magic-world? Why not hedge your bets and explore other methods? Pinning the survival of your entire society on one teenager seems like a particularly ill-advised move. Tangentially, why not study (and later attempt to reproduce) what makes Harry immune to a ton of otherwise-lethal magic stints?

Then, after defeating the Most Evil And Worst Person In Wizardom, Harry takes his wealth of insane experiences and decides to become... a magic cop (if you're really The Very Special Main Character maybe you should write and share your experiences/insights with everyone instead of issuing wizard parking tickets?).