No, genetics, parentage, and luck alone cannot produce Captain America, Hancock, or Superman, to any degree
It's important to remember that superheros are popular because everyone can relate to the dream of being something more than they are... something that can overcome the many challenges, temptations, obstacles, and set-backs in our lives. We all know that can't happen, but it's a lot of fun to wish we could. I call it, "the desire to do great things."
What's funny is that people do great things all the time. Great acts of kindness, strength, mental prowess, sacrifice, fortitude, speed... they just don't usually rank to the level of a good Mavel Comics movie.
And that means you can do it!
It's your story! What parents in the world wouldn't wish their child could become something that rises above the status-quo? I encourage you to make the choice to allow two ordinary people to create an extraordinary child — someone who can do impressive things, someone who leaves people wondering, "how'd he do that?"
Frankly, I have my moments asking that question. How did Stephen Hawking, with all his physical limitations, conceive in his imagination the wonders of our physical universe? How does Michael Phelps (who is darn close to a genetically perfect swimmer) win his medals? How on earth does Usain Bolt run that fast?
And in your story, you need only push the abilities of your character just a bit more to make them simply superhuman. Granted, the further away from the average you push them, the less believable it will be... but you'd be surprised how far that envelope can be pushed. Pretty much everyone has the desire to do great things and the desire for their children to do great things.
Make it so! Pick up your pencil, or sit at your computer, or turn on your voice recorder, and write a wonderful story. Sometimes, a good story is more important than the reality in which it resides.
Go watch the movie The Age of Adaline. It describes an environmental circumstance that is impossible from the perspective of today's science, but the point of the story isn't that circumstance. It merely "justifies" the conditions of the story. It's a good example of how to tell the kind of story you're writing.