Odds of Getting In
Succeeding in this field takes two things. One: a huge amount of work and sacrifice, and Two: a huge amount of luck. It's true that anyone with approximately the right body type and enough drive and focus can compete in lower-level events...but they will only earn a few hundred bucks per fight. At that rate, you've got to fight pretty often, which can wear you down. You've got to make a name for yourself as quickly as possible to move up in the popularity and pay scale.
The most famous boxers are not necessarily the very best—just the ones who people want to watch. The name of the game is personality, because the game is fueled by cash from endorsements. You know you've gone pro when your paycheck comes mostly from the companies you endorse, instead of the venue you fight at.
College or the military are both excellent places to start, because many universities and most branches of the military have a boxing team. There you can get some free training and test yourself against worthy opponents in a well-regulated setting. Regardless, you'll also have to join the gym near you that has a reputation for training pro fighters.
You'll need a manager who knows the biz well, and can get you in the ring with good fighters. Once everyone knows what a beast you are, all you have to do is not let them down by continuing to beat increasingly famous people. Easy peasy, right?