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How does Captain America lift Thor's hammer? In Avengers: Age of Ultron, he is not worthy but how he is worthy in this film.

It was always unclear why Captain America couldn't lift Mjolnir in Age of Ultron.

Was he not worthy at all? Unlikely; it's Captain America after all, worthiness goes with the character, his MCU version at least. Plus, Mjolnir did move. (Note that in the comics, Cap has wielded Mjolnir)

Was he not completely worthy yet? Possibly. After all, there is still room for the Avengers to improve.

Was he actually refraining? By Endgame, this is the most likely. There's been talk about Captain America realising he could lift Mjolnir, but wouldn't, not to create an awkward situation for Thor. Thor was baffled at the sight of Mjolnir moving... And by Endgame, when Steve calls upon Mjolnir, he shouts:

I knew it!

Meaning he had more than suspicions​ about Captain America being worthy.

Because, he was willing to sacrifice himself to protect others.

The reason why Cap managed to do so is already explained in Thor Trilogy. When Thor was unproved of worthy in Thor when he committed a war which could lead to deaths of many. However, when he was willing to sacrifice himself for those who he loved by the end of the film, he proved himself worthy. Even Jane was able to lift it since he was going to sacrifice herself for Asgardians, who hated her at that time.

For the same reason, Captain America was also worthy to lift the hammer. However, the main question is why he couldn't do this in Age Of Ultron. The reason behind this is that he could lift Mjolnir at that time and even it moves a little, but he saw the look at Thor's face and decided not to make him feel devastated by the fact that a mortal can lift Mjolnir.

However, the move of Mjolnir did make Thor suspicious which he became sure when he saw Cap lifting it in Endgame and that's why he says "I knew it". In Endgame, Cap didn't have any choice but to use Mjolnir when he saw Thor being defeated by Thanos.