Odds of Getting In
Good news: there are literally millions of food service jobs across the country (source). That means at least a few dozen-thousand job openings at any one time. As long as you're able to string words together in generally cohesive sentences and can carry at least two plates at a time, you'll find someone willing to give you a shot.
Once you've got the basics down, you're pretty much set to get a serving job whenever you feel like it.
However, the chances of landing a job at a primo establishment are much less likely. Restaurants that cater to top-notch clientele often look for highly-seasoned and incredibly dependable staff, so you may have to put in many years at a lesser quality restaurant before you'll even be considered. It's all about paying your dues.
And with the money you'll be making up until then, your dues might be the only thing you can actually afford to pay.