Phil Coulson joins SHIELD at age eleven under circumstances that are still highly classified. He tells people that he snuck in under the radar. This is entirely true, if by radar you mean in the trunk of his dad's car. It was easier to draft him into SHIELD than do anything else by that point. Dad calls it a lost cause. Father calls it about time. Phil calls it his after-school job.
Most SHIELD agents are not recruited by their fathers, but Phil's never been most people. Ignore the special agent "track you down by your sneaker prints when you run away from home in second grade" part of it all. You don't get to be most people when you grow up in the 70s with your bio-dad being white and your awesome-dad being black. And then especially not when they give you your mother's last name for your own protection.
Phil grows up with aliens being real and his parents being superheroes and a very strict nine o'clock bedtime. These things have a certain effect. For one, Phil knows exactly how to pass notes in class without being caught.
When Canton Everett Delaware The Third and Nicholas Fury finally do get married, it's 2012. The Doctor shows up with some of his friends. Pepper and Amy hit it off immediately. The Avengers take turns pulling Tony Stark back from his attempts to steal the TARDIS and take it apart to see how it works. Barton wears a cupid costume and threatens to shoot people, blaming it on the lack of bouquet throwing.
Phil surrenders the rings and holds his breath. His parents get married. Nothing blows up. He exhales.
The Doctor pats Phil's parents on their shoulders. "I knew you crazy kids would make it," he says.