Karla here…
Imagine everything you’ve ever known and loved is gone. Your comrades in arms, your best friend, even the girl you had a crush on are either dead or have moved on. Time and the world carried on without you, while you were asleep, and you have no choice but to get use to it. Captain America is a man out of time and out of touch with the modern age. The brightest technological advancement of his era was the atomic bomb. Now he has to deal with a brighter, nosier, and harsher world. The deleted scene shows Captain America trying to cope and failing.
We see him watching newsreel footage of himself landing on Omaha Beach on D-Day, fighting Nazis, and speaking with Gen. Eisenhower all on a laptop. You can see he isn’t adjusting well. Old dossiers on his friends, The Invaders, are all marked deceased, except for Peggy Carter. He wants to call her until he sees his shiny new cordless phone and then he gives up.
He walks the streets of New York City and can’t even tell when a pretty girl is flirting with him. Stan Lee has verbally slapped him to get him to realize this, and then cut to a boxing gym with Nick Fury making you an offer to save the world.
I can see why Joss Whedon went with the opening he chose. This opening would have been too bleak and too slow. I think the scene in the boxing gym conveys Captain America/Steve Roger’s bout with solitude.
Source: Latino Review