Well before back in time to grow old with Peggy Carter (Hayley Atwell). The moment served as a great closing to Steve's story, but then left the world without a Captain America.
This only lasted a few seconds in real-time though, as old Steve appeared not too long after regular Steve entered the Quantum Realm. His emergence happened as Smart Hulk (Mark Ruffalo) and Sam Wilson aka Falcon (Anthony Mackie) began arguing over what went wrong. But, Bucky Barnes (Sebastian Stan) was the first to notice Steve sitting on a nearby bench and told Falcon to go talk to him. This proved to be an important moment in Sam's life, as Steve gave him his own instead of giving the shield to Bucky), Steve actually explained why he made this choice moments before.
Right before Steve enters the Quantum Realm again, he exchanges pleasantries with Bucky and Sam. Sam offers to go with Steve on this journey and Steve's response is the answer fans have been looking for. He says, "You're a good man Sam. This one's on me though." It may not seem like much at first, but Sam being a "good man" is exactly why Steve chose him to be the new Captain America. It is a callback to what Abraham Erskine (Stanley Tucci) said to Steve in Captain America: The First Avenger when he asked why he was chosen to undergo the supersoldier experiment. Erskine said, "Whatever happens tomorrow, you must promise me one thing. That you will stay who you are, not a perfect soldier, but a good man."
While Captain America has always had super strength, super speed, and a variety of other enhanced abilities, the core of him as a character is his morality. Steve Rogers is a good man even without his superpowers; he was jumping on grenades back when he was still a scrawny wannabe soldier. Sam may not have actual superpowers like Steve - or Bucky, for that matter - but he does have the same moral com and the strength of his character will no doubt play a significant part in Phase 4's new show. Sam has always been willing to fight with Steve no matter what because of their like-mindedness. And even though Steve already made up his mind by this time to appoint Sam as his predecessor, him once again offering his services results in this great moment and subtle explanation of his decision.
Even if this callback didn't happen, the choice between Falcon and Bucky as the new Captain America should've been a no brainer for Steve. This isn't because Bucky is not a "good man" in any way, but rather simply because Sam is better equipped to take on this role. Bucky still has Hydra codes potentially swirling in his subconscious and has a known history as an assassin, even though the agreed Falcon was the obvious choice.
Now that Falcon is set to be Captain America in the MCU moving forward, The Falcon and The Winter Soldier will be the first chance to see him tested in this capacity. The marketing for the show and the reveal of the new Captain America, played by Wyatt Russell has already indicated that Sam becoming Cap will not be a decision that is universally approved, so his good nature may be called into question early on. But, with everything that Sam has shown to this point and what Steve sees in him, hopefully, he'll continue to be a good man as he wears the red, white, and blue.
