Avengers: Endgame was full of moments that made the audience stand and cheer. However, the biggest audience-pleasing moment of the film had to be when Captain America finally wielded Thor's hammer, Mjolnir. The moment was teased to great effect back in Avengers: Age of Ultron and this was the big pay off that proved Cap was worthy.
While that climactic and desperate fight against Thanos was the moment Cap took up Mjolnir, it's likely he has been worthy for quite some time. Few characters in the MCU have proven to be as selfless and heroic and Captain American. This moment was a long time coming and there's plenty of evidence to show how he earned the right. Here are the moments that proven Captain America was always worthy to wield Mjolnir.
Stopping The Helicopter
Steve Roger's relationship with his old friend Bucky is a big factor in defining him as a hero. Bucky is one of the few people who knew and respected him before he was Captain America and therefore he is willing to sacrifice a lot to help his friend when he becomes The Winter Solider.
After Bucky is brainwashed again and fleeing the scene in a helicopter, Steve makes a desperate and incredibly impressive attempt to stop him. Not only is it a feat of immense strength watching him hold back the helicopter, but it's emotionally powerful as he is using everything he has to keep his friend from further damaging his life.
Fighting The Bully
The super solider serum that Steve took made him stronger, faster and taller, but everything that made Captain America a hero came from what Steve already had within himself. He is not a violent or angry person, but he is also not one to back down from a fight. And he doesn't like bullies.
A fine example of the kind of hero Steve has always been comes when he stand up to the loudmouth who is disrespecting the men serving in the war. Despite being totally out matched, Steve refuses to back down, delivering the line that would define his character, "I could do this all day".
Not Fighting Bucky
Again, Steve's allegiance to Bucky and his wish to see him saved highlights his qualities as a hero. Steve knows Bucky stands between him and saving the day and therefore he needs to fight his friend, however painful it may be.
One Hydra is defeated, Steve stands down. He doesn't know if Bucky is still inside that killer mind or not, but he is willing to die to help bring Bucky back. Letting go of his shield, Steve surrenders himself to the Winter Soldier and takes a severe beating as a result. But he manages to reconnect with Bucky's damaged mind.
Leading The Avengers
Captain America is not be the strongest Avenger, or the smartest. And he didn't see eye-to-eye with all the other heroes from the beginning. Yet when the world is at stake, there is only one member of the team the rest turn to for leadership.
Cap isn't power hungry or one to demand control of a situation, but he does inspire those around him. Though the enemy outnumbers them, Cap does not blink in the face of the invading Chitauri. He springs into leader mode immediately, giving out orders and directing the defense of the city. His leadership of the team throughout the movies and in their darkest moment proves he is the greatest Avenger.
Giving Up His Shield
Apart from being a physics-defying super weapon, Captain America's shield is an extremely important symbol. By carrying the shield, Cap is accepting that he is representing something bigger than himself and naming himself as protector. So to lose that symbol by choice is a significant moment for the character.
Cap and Iron Man get into a brutal fight in Civil War where, once again, Cap is just trying to save Bucky. When Tony is defeated he tells Steve he doesn't deserve to carry that shield. While Steve won't abandon what he thinks is right, he concedes that he is no longer Captain America.
Running Into Battle
The battle of Wakanda in Infinity War was one of the most high-stakes fights our heroes had ever been involved in and they were up against a frightening enemy. And still, Steve did not hesitate to be at the front of that army and the first into battle. With T'Challa right by his side, Steve charges far ahead of the rest of them and these two warriors begin taking on the enemy.
In is a moment Steve completely shares with T'Challa but it is no less heroic. While there are plenty of heroes rushing into that battle, to see those two lead the charge by themselves was a moment that still gives us chills.
Volunteering For The Army
Long before he had the powers of Captain America, Steve still had the heart of a hero. It takes an extremely brave person to volunteer to fight for their country and Steve showed his bravery several times over. Despite being told he was unfit for service, he refused to give up. In his mind, it wasn't right that he stay at home while others risked their lives.
What makes his volunteering even more heroic is that he isn't seeking glory like some. While he won't back down from a fight, Steve isn't one to look for one either. He simply sees injustice in the world and feels that he needs to fight against it somehow.
Jumping On The Grenade
Given Steve's physique prior to the super solider transformation, some people were understandably skeptical that this scrawny kid was the right one to save the world. Tommy Lee Jones' Col. Phillips tries to demonstrate, Steve isn't the hero they need only to be immediately proven wrong. Phillips tosses a dummy grenade in the middle of the platoon's training exercise. While everyone scatters, Steve leaps onto the grenade to save everyone else.
Some might see it as the act of a fool, but it shows Steve's immediate reaction is always in the interest of others rather than himself.
Standing Up To Thanos
Thanos is shown to be the most powerful villain the Avengers have ever come up against. In the very first scene of Infinity War, he easily beats Hulk in a fight and later goes up against an entire team of heroes and beats them all. So when the Mad Titan shows up in Wakanda, the remaining Avengers have little chance of beating him. But that doesn't stop Cap from trying.
As the team tries to hold Thanos back from Vision, he takes them out one-by-one until only Cap is left standing. In that desperate moment, Cap uses all his strength to hold Thanos back for just another moment, a feat that surprises Thanos himself. It is another example of Cap refusing to give in and putting everything he has into saving the day.
Giving His Life
In the first Thor, the thing that proves Thor is still worthy of Mjolnir is that he sacrifices his life to stop the Destroyer. It is in fact a heroic moment for the character, but if self-sacrifice is all it takes to lift the hammer, pretty much every Avenger would be worthy. It is perhaps Cap who is the most worthy in that regard.
After defeating Red Skull in First Avenger, Cap realizes he must crash the plane he's one into the water in order to save innocent lives. While the crash doesn't kill him, he does lose his life, waking up in a world where he is alone. But it is a sacrifice Cap knew he had to make.